OVERVIEW
TIME 
MONDAY 12/10 
Session Chair 
8:00 – 8:30 
Coffee & Bagel 

8:30 – 9:10 
Inv. Talk 1: Andrew Viterbi 
Terrence Sejnowski 
9:10 – 10:30 
Session 1: Theory & Algorithms I 
Erkki Oja 
10:30 – 10:50 
Coffee break 

10:50 – 12:30 
Session 2: Applications I 
Luis Almeida 
12:30 – 2:00 
Lunch 

2:00 – 2:40 
Inv. Talk 2: Mohan Trivedi 
TeWon Lee 
2:40 – 4:00 
Session 3: Theory & Algorithms II 
Lars Kai Hansen 
4:00 – 4:20 
Tea break 

4:20 – 5:50 
Poster 1 
Eric Moreau, TzyyPing Jung 
5:50 – 6:30 


7:00 – 8:00 
Social Event & Snacks 

8:00 – 9:00 
Poster 2 
Seungjin Choi, TeWon Lee 
TIME 
TUESDAY 12/11 
Session Chair 
8:00 – 8:30 
Coffee & Bagel 

8:30 – 9:10 
Inv. Talk 3: Michael Jordan 
Tony Bell 
9:10 – 10:30 
Session 4: Biomedical Signal Processing 
Scott Makeig 
10:30 – 10:50 
Coffee break 

10:50 – 12:30 
Session 5: Theory & Algorithms III 
J.F. Cardoso 
12:30 – 2:00 
Lunch 

2:00 – 2:40 
Inv. Talk 4: Gilles Laurent 
Christian Jutten 
2:40 – 4:00 
Session 6: Applications II 
Scott Douglas 
4:00 – 4:20 
Tea break 

4:20 – 5:50 
Poster 3 
TzyyPing Jung, TeWon Lee 
5:50 – 6:30 
Inv. Talk 5: Robert HechtNielsen 
Javier Movellan 
7:00 – 8:00 
Banquet Dinner 

8:00 – 9:00 
Tony Bell Banquet Talk 
Terrence Sejnowski 
TIME 
WEDNESDAY 12/12 
Session Chair 
8:00 – 8:30 
Coffee & Bagel 

8:30 – 9:10 
Inv. Talk 6: Bhaskar Rao 
TeWon Lee 
9:10 – 10:30 
Session 7: Convolved Sources 
Andrzej Cichocki 
10:30 – 10:50 
Coffee break 

10:50 – 12:30 
Session 8: Nonlinear Representation 
Juha Karhunen 
12:30 – 2:00 
Lunch (Salk) 

2:00 – 2:40 
Inv. Talk 7: Christof Koch 
Barak Pearlmutter 
2:40 – 4:00 
Session 9: Speech Signal Processing 
Lars Kai Hansen 
4:00 – 4:20 
Tea break 

4:20 – 5:50 
Inv. Talk 8: Geoffrey Hinton 
Terrence Sejnowski 
5:50 – 6:00 
Closing remarks 

8:15
– 8:30 Opening Remarks: Terrence Sejnowski (CNL, The Salk Institute,
INC, UCSD)
8:30 – 9:10 Inv.
Talk 1 Andrew Viterbi (Qualcomm, Inc)

9:10 – 10:30 Session 1: Theory & Algorithms I

10:10 10:30 Spotlights

10:30 – 10:50 Coffee Break
10:50 – 12:30 Session 2: Applications I

12:10 – 12:30 Spotlights

12:30 – 2:00 Lunch
2:00 – 2:40 Inv.
Talk 2  Mohan Trivedi (UCSD)

2:40 – 4:00 Session 3: Theory & Algorithms II

3:40 – 4:00 Spotlights

4:00 – 4:20 Tea Break
7:00 – 8:00 Social Event & Food
8:30 – 9:10 Inv.
Talk 3  Michael Jordan (UC
Berkeley)

9:10 – 10:30 Session 4: Biomedical Signal Processing

10:10 – 10:30 Spotlights

10:30 – 10:50 Coffee Break
10:50 – 12:30 Session 5: Theory & Algorithms III

12:10 – 12:30 Spotlights

12:30 – 2:00 Lunch
2:00 – 2:40 Inv.
Talk 4  Gilles Laurent
(Caltech)

2:40 – 4:00 Session 6: Applications II

3:40 – 4:00 Spotlights

4:00 – 4:20 Tea Break
5:50 – 6:30 Inv.
Talk 5  Robert Hecht Nielsen
(HNC, Inc.)

7:00 – 8:00 Banquet Dinner
8:30 – 9:10 Inv.
Talk 6  Bhaskar Rao

9:10 – 10:30 Session 7: Convolved Sources
9:10 – 9:30 Pierre Comon, Eric Moreau, Ludwig Rota
[29]
9:30 – 9:50 M. Kawamoto, Y. Inouye, A. Mansour, and
R.W. Liu [92]
9:50 – 10:10 Naoki Saito, Bertrand Benichou [46] 
10:10 – 10:30 Spotlights

10:30 – 10:50 Coffee Break
10:50 – 12:30 Session 8: Nonlinear Representation
10:50 – 11:10 Alexandre Iline, Harri Valpola, Erkki Oja [12]
11:10 – 11:30 Harri Valpola, Tapani Raiko, Juha Karhunen [107]
11:30 – 11:50 Torbjorn Eltoft, Orjan Kristiansen [51]
11:50 –
12:10 Kiyotoshi Matsuoka, Satoshi
Nakashima [99] 
12:10 – 12:30 Spotlights
Sophie Achard,
Dinh Tuan Pham, Christian Jutten [50]
Douglas R.
Hundley, Michael J. Kirby, Markus G. Anderle [115]
Andreas Ziehe, Motoaki Kawanabe, Stefan Harmeling, KlausRobert Muller [120]
Russell H. Lambert, Marcel Joho, Heinz Mathis [85]

12:30 – 2:00 Lunch (at the Salk Institute)
2:00 – 2:40 Inv.
Talk 7  Christof Koch (Caltech)

2:40 – 4:00 Session 9: Speech Signal Processing
2:40 – 3:00 Tomasz Rutkowski, Andrzej Cichocki, Allan Kardec Barros [86]
3:00 – 3:20 Frederic Abrard, Yannick Deville, Paul White [53]
3:20 – 3:40 Sergio Cruces, Andrzej Cichocki, Shunichi Amari [82] 
3:40 – 4:00 Spotlights
Scott Rickard,
Radu Balan, Justinian Rosca [84]
Andrzej Cichocki, Adel Belouchrani [3]
Kamran Rahbar, James P. Reilly [55]
Radu Balan, Justinian Rosca, Scott Rickard [88] 
4:00 – 4:20 Tea Break
4:20 – 5:30 Inv.
Talk 8  Geoffrey Hinton
(University of Toronto)

5:30 Closing remarks
Andrew Viterbi (Qualcomm, Inc.)
For over half a century, information theorists and communication engineers have been refining methods to transmit reliably over noisy channels at rates ever closer to the Shannon Capacity limit. The class of lowdensity parity check (LDPC) codes, originally proposed by Gallager (1963), have been shown within the last year to be capable of approaching within epsilon of this elusive goal. We describe the nature of the codes and particularly the iterative decoding algorithms which make this performance possible. We then demonstrate examples of the analysis, known as density evolution, which establishes the decoder’s convergence to the correct estimate.
Dr. Andrew Viterbi is a cofounder and retired Vice Chairman and Chief Technical Officer of QUALCOMM Incorporated. He spent equal portions of his career in industry, having also cofounded a previous company, and in academia as Professor in the Schools of Engineering first at UCLA and then at UCSD, at which he is now Professor Emeritus. He is currently president of the Viterbi Group, a technical advisory and investment company. His principal research contribution, the Viterbi Algorithm, is used in most digital cellular phones and digital satellite receivers, as well as in such diverse fields as magnetic recording, voice recognition and DNA sequence analysis. In recent years he has concentrated his efforts on establishing CDMA as the multiple access technology of choice for cellular telephony and wireless data communication. Dr. Viterbi has received numerous honors both in the U.S. and internationally. Among these are four honorary doctorates as well as memberships in the National Academy of Engineering, the National Academy of Sciences and the American Academy of Arts and Sciences. He has received the Marconi International Fellowship Award, the IEEE Alexander Graham Bell and Claude Shannon Awards , the NEC C&C Award, the Eduard Rhein Award and the Christopher Columbus Medal.
Awareness of the space and activities taking place in them are essential requirements of Intelligent Spaces. In this presentation we will describe research efforts directed towards the realization of such intelligent spaces, by using visual and audio sensor networks imbedded in the environment to make them aware of the space and activities taking place in them. The visual awareness is derived utilizing multiple video streams acquired from both the traditional rectilinear as well as the omni directional sensor arrays. This "active" vision system systematically processes the signal, focus of attention, and context level information. This allows the spaces to derive and continuously maintain an awareness of the identities, locations, and activities of various entities (e.g. people, vehicles, or avatars) inhabiting these spaces. We will present results of our recent research involving "indoor", outdoor and mobile intelligent spaces. Hopefully, these efforts will underline the important role that robust feature extraction and decision theoretical frameworks, like ICA, can play as well as the exciting opportunities in the development of a wide range of intelligent (or "smart") systems.
Mohan M. Trivedi is a Professor in the Electrical and Computer Engineering Department of the University of California, San Diego where he serves as the Director of the Computer Vision and Robotics Research Laboratory (http://cvrr.ucsd.edu). He and his team are engaged in a broad range of research studies in active perception and novel machine vision systems, intelligent (“smart”) environments, distributed video networks and intelligent systems. At UCSD Trivedi also serves on the Executive Committee of the California Institute for Telecommunication and Information Technologies, Cal(IT)^{2}, leading the team involved in the Intelligent Transportation and Telematics project. He also serves as a charter member of the Executive Committee of the University of California Systemwide Digital Media Innovation (http://www.dimi.ucsb.edu/) (DiMI) Program. Trivedi serves as the EditorinChief of Machine Vision and Applications, the official journal of the International Association of Pattern Recognition. He has published extensively and has edited over a dozen volumes including books, special issues, video presentations, and conference proceedings. He servers regularly as a consultant to various national and international industry and government agencies. Trivedi is a recipient of the Pioneer Award (Technical Activities) and the Meritorious Service Award of the IEEE Computer Society and the Distinguished Alumnus Award from the Utah State University. He is a Fellow of the International Society for Optical Engineering (SPIE). He has been elected to the honor societies of Phi Kappa Phi, Tau Beta Pi, and Sigma Xi. He is listed in the Who's Who in the Frontiers of Science and Technology, Who's Who of in American Education, American Men and Women of Science, Who’s Who in the World and other similar publications.
Michael Jordan (University of California, Berkeley)
Francis R. Bach and Michael I. Jordan (University of California, Berkeley)
We present a new class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence. On the other hand, building on recent developments in kernel methods, we show that these criteria and their derivatives can be computed efficiently. Minimizing these criteria leads to flexible and robust algorithms for ICA. We illustrate with simulations involving a wide variety of source distributions, showing that our algorithms outperform many of the presently known algorithms.
Michael I. Jordan is Professor in the Department of Electrical Engineering and Computer Science and the Department of Statistics at the University of California at Berkeley. He received his Masters in Mathematics from Arizona State University, and earned his PhD in Cognitive Science from the University of California, San Diego. He was a professor at the Massachusetts Institute of Technology from 1988 to 1998. Prof. Jordan's research has spanned a number of fields, including psychophysics, computer science and statistics. He has published over 140 research articles in these areas. In psychophysics, he is known for his work on the role of predictive forward models in human motor control. In computer science and statistics, he has been a leading figure in the area of probabilistic graphical models, a marriage of graph theory and probability theory that is of wide current interest. Prof. Jordan has given invited plenary lectures at numerous international conferences, including the International Conference on the Mathematical Theory of Networks and Systems, the International Joint Conference on Neural Networks, the ACM Conference on Computational Learning Theory, and the Conference on Uncertainty in Artificial Intelligence.
Gilles Laurent (California Institute of Technology)
The study of brain function has for a long time ignored the potential importance of neural circuit dynamics. I will examine this issue in the context of olfactory processing. The talk will summarize our data and its interpretation on slow temporal patterning and fast oscillatory synchronization in olfactory circuits. I will show that slow patterning allows input decorrelation (and thus optimization of the use of coding space), while synchronization plays an essential role in the sparsening of representations, a step probably essential for memory formation and pattern matching.
French citizen, born and grown up in Morocco, educated in France: Veterinary medicine + PhD (Neuroethology). Postdoc in Cambridge (Neuroscience, with Malcolm Burrows) for 4 years. At Caltech since 1990, where I am now Professor of Biology and Computation and Neural Systems.
Robert HechtNielsen (HNC & UCSD)
A RealTime LanguageKnowledgeDependent Solution to the Cocktail Party Problem
Cortronic architectures consist of linked classical associative memory structures. Learning is carried out such that associative recalls optimize significance; a new informationtheoretic quantity. Information processing algorithms (thought processes), which can be learned by rehearsal practice, are sequences of regional feature detector and associative fascicle activations analogous to the muscle contraction sequences of movement (thought is viewed as a phylogenetic outgrowth of movement). In the cocktail party problem a cortronic architecture is used at each moment to predict possible next sound utterances. The feature detectors associated with the detection of these sounds are sensitized to form an expectation. If any of the expected sounds arrives the relevant feature detectors respond and this lowlevel input is sent on to higher levels for analysis. This analysis yields an ongoing output of what is being said by the attendedto speaker (and an ongoing feedback of predictive expectation). There is no source separation, per se, since other sounds present are not detected in the first place. The characteristics of this cocktail party solution match the known characteristics of the human solution at many points; including a lack of processing delay and a need to guess (or momentarily increase the SNR) to start the process.
Affiliations:
(1985  Present) University of California, San Diego
[Teaching Professor]
Program in Computational Neurobiology
Institute for Neural Computation
Department of Electrical and Computer Engineering
(1986  Present) HNC Software Inc. [Successful Capitalist]
Honors:
Graduate Teaching Award
IEEE Fellow
IEEE Neural Networks Pioneer Award
Education:
Ph.D., Mathematics, Arizona State University
Tony Bell (The Salk Institute & UCSF)
I will examine the notion that the goal of the perceptual system is to build a model of how our mixedup experiences are the result of changes in external objects. There will be examples drawn from mathematics and from neuroscience.
Tony Bell was raised in Northern Ireland and studied computer science and philosophy at the University of St Andrews in Scotland. He received his PhD from the Free University of Brussels for a thesis on "Selforganising Neural Dynamics" in 1993. He did his postdoctoral work on ICA with Terry Sejnowski's Computational Neurobiology lab at the Salk Institute in San Diego. He has also worked in the San Francisco area.
Bhaskar D. Rao (University of California, San Diego)
This paper examines the theoretical and computational issues that arise in signal processing problems with the sparseness constraint in several important application domains. Due to the NPcomplete nature of the optimization problem, several suboptimal methods with lower computational complexity have been developed to compute sparse solutions. First, sequential selection methods such as the Matching Pursuit algorithm are discussed. Then, algorithms based on minimizing suitable diversity measures are presented. In particular, algorithms such as FOCUSS (FOCal Underdetermined System Solver) that are based on a factored representation of the gradient and employ an Affine Scaling Transformation are discussed. Finally, some observations are made about the relative performance of the algorithms.
Bhaskar D. Rao received the B. Tech. degree in electronics and electrical communication engineering from the Indian Institute of Technology, Kharagpur, India, in 1979, and the M.S. and Ph.D. degrees from the University of Southern California in 1981 and 1983 respectively. Since 1983, he has been with the University of California, San Diego, where he is currently a Professor in the Electrical and Computer Engineering department. He is a fellow of IEEE and has been a member of the Statistical Signal and Array Processing technical committee. He is currently a member of the signal processing theory and methods technical committee. His interests are in the areas of digital signal processing, estimation theory, and optimization theory, with applications to digital communications, speech signal processing, and humancomputer interactions.
Christof Koch (California Institute of Technology)
Responses Of Single Neurons In The Human Medial Temporal Lobe During Visual
In collaboration with Dr. Itzhak Fried at UCLA Medical School, we studied the visual properties of single neurons in the medial temporal lobe of patients with intractable epilepsy. Based on clinical criteria, intracranial electrodes were implanted by Dr. Fried to localize seizure foci for surgical resection. Probes were stereotactically placed in bilateral medial temporal lobe targets including hippocampus, amygdala, entorhinal cortex and parahippocampal gyrus. We recorded the activity of individual neurons while patients viewed pictures of faces, objects, patterns and animals on a monitor, when the patients were asked to imagine these pictures with closed eyes and during both rivalry and flash suppression. In this largescale study of visual responses in more than 800 units in conscious humans, we show that individual neurons respond very selectively to visual stimuli from different natural categories, including faces, We show that a subset of these cells have the identical selectivity during imagery, We also show that the majority of the visually selective cells follows the percept during flash suppression. None of these neurons were active for a perceptually suppressed stimulus.
I was born on November 13, 1956 in Kansas City, Missouri. I subsequently grew up in Amsterdam/Holland, Bonn/Germany, Ottawa/Canada, and Rabat/Marocco where I graduated from the Lycèe Descartes with a French Baccalaurèat (Section C) in 1974. I studied Physics and Philosophy in Tübingen, Germany, and was awarded my Master of Physics in 1980 and my PhD (Nonlinear information processing in dendritic trees of arbitrary geometry) from the MaxPlanckInstitut for Biological Cybernetics in Tübingen in 1982. My "DoctorFather" was Prof. Tomaso Poggio, now at MIT. After 4 years as a postdoctoral fellow at the Artificial Intelligence Laboratory and at the Department of Psychology at MIT, I joined Caltech's newly started Computation and Neural Systems option, where I have been ever since (now as a Professor of Computation and Neural Systems), running the KLab as well as being the Executive Officer of CNS.
Geoffrey Hinton (University of Toronto)
We present a new way of interpreting ICA as a probability density model and a new way of fitting this model to data. The advantage of our approach is that it suggests simple, novel extensions to overcomplete, undercomplete and multilayer nonlinear versions of ICA.
Geoffrey Hinton received his BA in experimental psychology from Cambridge in 1970 and his PhD in Artificial Intelligence from Edinburgh in 1978. He did postdoctoral work at Sussex University and the University of California, San Diego and spent five years as a faculty member in the Computer Science department at CarnegieMellon University. He then moved to Toronto where he was a fellow of the Canadian Institute for Advanced Research and a Professor in the Computer Science and Psychology departments. He is a former president of the Cognitive Science Society and a fellow of the Royal Society of Canada and of the American Association for Artificial Intelligence. In 1992 he won the ITAC/NSERC award for contributions to information technology. A simple introduction to his research can be found in his articles in Scientific American in September 1992 and October 1993.
He does research on ways of using neural networks for learning, memory, perception and symbol processing and has over 100 publications in these areas. He was one of the researchers who introduced the backpropagation algorithm that is now widely used for practical applications. His other contributions to neural network research include Boltzmann machines, distributed representations, timedelay neural nets, mixtures of experts, and Helmholtz machines. His current main interest is in unsupervised learning procedures for neural networks with rich sensory input
JeanFrancois Cardoso
The Three Easy Routes to Independent Component Analysis; Contrasts and Geometry
Blind separation of independent sources can be achieved by exploiting non Gaussianity, non stationarity or time correlation. This paper examines in a unified framework the objective functions associated to these three routes to source separation. They are the ‘easy routes’ in the sense that the underlying models are the simplest models able to capture the statistical structures which make source separation possible. A key result is a generic connection between mutual information, correlation and marginal ‘non properties’: non Gaussianity, non stationarity, non whiteness.
Deniz Erdogmus, José C. Príncipe
An OnLine Adaptation Algorithm for Adaptive System Training with Minimum Error Entropy: Stochastic Information Gradient
We have recently reported on the use of minimum error entropy criterion as an alternative to minimum square error (MSE) in supervised adaptive system training. A nonparametric estimator for Renyi’s entropy was formulated by employing Parzen windowing. This formulation revealed interesting insights about the process of information theoretical learning, namely information potential and information forces. Variants of this criterion were applied to the training of linear and nonlinear adaptive topologies in blind source separation, channel equalization, and chaotic timeseries prediction with superior results. In this paper, we propose an online version of the error entropy minimization algorithm, which can be used to train linear or nonlinear topologies in a supervised fashion. The algorithms used for blind source separation and deconvolution can be modified in a similar fashion. For the sake of simplicity, we present preliminary experimental results for FIR filter adaptation using this online algorithm and compare the performance with LMS.
Riccardo Boscolo, Hong Pan, Vwani P. Roychowdhury
We introduce a novel approach to the blind signal separation (BSS) problem that is capable of jointly estimating the probability density function (pdf) of the source signals and the unmixing matrix. We demonstrate that, using a kernel density estimation based Projection Pursuit (PP) algorithm, it is possible to extract, from instantaneous mixtures, independent sources that are arbitrarily distributed. The proposed algorithm is nonparametric, and unlike conventional Independent Component Analysis (ICA) frameworks, it requires neither the definition of a contrast function, nor the minimization of the highorder crosscumulants of the reconstructed signals. We derive a new method for solving the resulting constrained optimization problem that is capable of accurately and efficiently estimating the unmixing matrix, and which does not require the selection of any tuning parameters. Our simulations demonstrate that the proposed method can accurately separate sources with arbitrary marginal pdfs with significant performance gain when compared to existing ICA algorithms. In particular, we are successful in separating mixtures of skewed, almost zerokurtotic signals, which other ICA algorithms fail to separate.
Noboru Murata
Properties of the Empirical Characteristic Function and its Application to Testing for Independence
In this article, the asymptotic properties of the empirical characteristic function are discussed. The residual of the joint and marginal empirical characteristic functions is studied and the uniform convergence of the residual in the wider sense and the weak convergence of the scaled residual to a Gaussian process are investigated. Taking into account of the result, a statistical test for independence against alternatives is considered.
Vincente Zarzoso, Asoke K. Nandi
A General Theory of ClosedForm Estimators for Blind Source Separation
We present a general theory for the closedform parametric estimation of the unitary mixing matrix after prewhitening in the blind separation of two source signals from two noiseless instantaneous linear mixtures. The proposed methodology is based on the algebraic formalism of bicomplex numbers and is able to treat both real and complex valued mixtures indiscriminately. Existing analytic methods are found as particular cases of the exposed unifying formulation. Simulations in a variety of separation scenarios— even beyond the noiseless twosignal case — compare, assess and validate the methods studied.
Yasu Matsuyama, Naoto Katsumata, Shuichiro Imahara
Convex Divergence as a Surrogate Function for Independence: The fDivergence ICA
The convex divergence is used as a surrogate function for obtaining independence of random variables described by the joint probability density. If the kernel convex function is twice continuously differentiable, this case reveals a class of generalized logarithm. This class of logarithms gives generalizations of the score function and the Fisher information matrix which are related to the CramerRao bound. Guided by these properties, independent component analysis (ICA) using the convex divergence is presented.Obtained algorithms use the past and/or future data. Software implementation is easy and beats the minimum mutual information ICA in the speed. Real world experiments on brain fMRI are also performed.
Dinh Tuan Pham
Contrast Functions for Blind Separation and Deconvolution of Sources
A general method to construct contrast functions for blind source separation is presented. It is based on a superadditive functional of class II applied to the distributions of the reconstructed sources. Examples of such functionals are given. Our approach permits exploiting the temporal dependence of the sources by using a functional on the joint distribution of the source process over a time interval. This yields many new examples and frees us from the constraint that the sources be non Gaussian. Contrasts functions based on cumulants requiring the orthogonality constraint is also covered. Finally, the case of convolutive mixtures is considered in relation with the problem of blind separationdeconvolution.
Maria Funaro, Erkki Oja, Harri Valpola
Artefact Detection in Astrophysical Image Data Using Independent Component Analysis
This paper is the first reported application of ICA on astrophysical image data. When studying farout galaxies from a series of consequent telescope images, there are several sources for artefacts that influence all the images such as camera noise, atmospheric fluctuations and disturbances, and stars in our own galaxy. For this problem, the linear ICA model holds very accurately, because the independence of such artefacts is guaranteed. Using image data on the M31 Galaxy, it is shown that several clear artefacts can be detected and recognized based on their temporal pixel luminosity profiles and independent component images. Once these are removed, it is possible to concentrate on the real physical events like gravitational lensing. ICA might provide a very useful preprocessing for the large amounts of available telescope image data.
Milutin Stanacevic, Gert Cauwenberghs, George Zweig
Gradient Flow Broadband Beamforming and Source Separation
We present and demonstrate a method for blind separation and bearing estimation of broadband traveling waves, impinging on a sensor array with dimensions smaller than the shortest wavelength in the sources. By sensing spatial and temporal gradients of the received signal, the problem of separating mixtures of timedelayed sources reduces to that of separating instantaneous mixtures of the gradient components of the sources using conventional tools of independent component analysis. Experimental results demonstrate realworld separation of speech in outdoors and indoors environments, using a planar array of four microphones within a 5 mm radius and analog circuits computing spatial and temporal derivatives.
Tapani Ristaniemi, Rui Wu
Mitigation of ContinuousWave Jamming in DSCDMA Systems Using Blind Source Separation Techniques
In this paper we consider blind interference suppression indirect sequence spread spectrum communication system with coexisting continuous wave (CW) jammer. Especially, blind source separation techniques are utilized. However, unlike in recent works only a single antenna element is employed. Numerical examples are given to illustrate achieved performance gains.
Xiaoan Sun, Scott C. Douglas
A Natural Gradient Convolutive Blind Source Separation Algorithm for Speech Mixtures
In this paper, a novel algorithm for separating mixtures of multiple speech signals measured by multiple microphones in a room environment is proposed. The algorithm is a modification of an existing approach for densitybased multichannel blind deconvolution using natural gradient adaptation. It employs linear predictors within the coefficient updates and produces separated speech signals whose autocorrelation properties can be arbitrarily specified. Stationary point analyses of the proposed method illustrate that, unlike multichannel blind deconvolution methods, the proposed algorithm maintains the spectral content of the original speech signals in the extracted outputs. Performance comparisons of the proposed method with existing techniques show its desirable properties in separating realworld speech mixtures.
Wolf Baumann, BertUwe Kohler, Dorothea Kolossa and Reinhold Orglmeister
Real Time Separation of Convolutive Mixtures
A new concept of combining conventional beamforming with independent component analysis (ICA) techniques and its implementation on a multi DSP system is presented. The system consists of two floating point digital signal processors TMS320C6701, an eight channel linear microphone array, an analog/digital converter board and a handheld control unit for stand alone operation. In the two system stages a sum and delay beamformer as well as a convolutive ICA algorithm are implemented. Due to the high performance of the digital signal processors, the systems achieves blind separation of two convolutive mixed sources in real time.
KiSeok Cho, SooYoung Lee
Implementation of INFOMAX ICA Algorithm with Analog CMOS Circuits
Independent Component Analysis algorithm based on infomax theory with natural gradient was implemented with a fullyanalog CMOS chip. Although one chip consists of 4 inputs and 4 outputs, the chip incorporates fullymodular architecture for multichip applications. The fabricated chip demonstrated improved SNRs for unknown speech mixtures.
Frank Meinecke, Andreas Zieche, Motoaki Kawanabe, Klaus R.Mueller
Assessing Reliability of ICA Projections – A Resampling Approach
When applying unsupervised learning techniques like ICA or temporal decorrelation for BSS, a key question is whether the discovered projections are reliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling methods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error. We demonstrate that this reliability estimation can be used to choose an appropriate ICAmodel, to enhance significantly the separation performance, and, most important, to mark the components that can really have a physical meaning. An application to data from an MEG 1 experiment underlines the usefulness of our approach.
Harold Szu
A Priori Maxent H(S) Independent Class Analysis (ICA) Vs. A Posteriori Maxent (V) ICA
Two mirror symmetric versions of the maximum entropy (MaxEnt) methodology are introduced and compared: (1) A posteriori MaxEnt Independent Component Analysis (ICA) H(V) was proposed by Bell, Sejnowski, Amari, Oja (BSAO) (early by Jutten & Herault, Comon and Cardoso (JHCC) in France). It is ambitious to factorize the unknown jointprobability density function (jpdf) using the post processing algorithm involving the sigmoidthreshold neurons' output V(x,y)= s([W]X(x,y)) of all image locations (x,y) in order to apply the pixelensemble averaged synaptic weight matrix [W] learning, ¶[W]/¶t=<¶H(V)/¶[W]>. The pixel ensemble average may be necessary to factorize the unknown jointpdf from multichannel data vector X(x,y). (2) A priori MaxEnt H(S) for independent class analysis (ica) is a compliment first step to the ambitious jointpdf factorization based on aposteriori MaxEnt H(V) ICA. Since ica is less ambitious to ICA in finding independent classes alone without their underlying pdf, we can derive from Gibb's statistics mechanics of independent classes of irradiation sources S_{j} by a priori MaxEnt H(S), which would be a flat equal class distribution if each were not constrained by the measurements by means of Lagrangian multipliers of force vector l_{i} and energy scalar (l_{o }1) for each pixel: ( Entropy Equation: See Paper).
Physically speaking, the long distance propagation by the speed of the light insures the line of sight local validity of a linear and instantaneous withinpixel mixture model of remote optical sensing. However, only the a priori MaxEnt H(S) ica can handle a large hyperspectral image data basis by the divideandconquer strategy without the pixel ensemble average that limits computationally the posteriori MaxEnt ICA algorithm. This strategy is possible because the radiation sources vector S(x_{o},y_{o}) per pixel contribute locally to the spectral image data per pixel X(x_{o},y_{o})= [A]S(x_{o},y_{o}), i.e. the irradiation collected within the foot print of the individual pixel (x_{o},y_{o}) will not mix with other neighborhood irradiation sources that will only contribute to their corresponding neighborhood pixels. Although this is basically true for any optical imaging, the post processing BSAO algorithm attempts to demix all pixel data [W]X in a batch mode that make it not scalable to large image data basis. Being a priori MaxEnt H(S) preprocessing, we can divide and conquer image size by applying ica pixel by pixel in real time. Furthermore, we have derived ab initio from it the usual sigmoid threshold logic S = s(l[A]) and the Hebbian learning ruled DA_{ij} =l_{i}S_{j}. We can thus conjecture any linear communication theorem that a linear matrix transform (e.g. associative memory [A] recall) between data X=[A]S and its independent classes under the constraint of comprehensive decomposition S_{j }S_{j }= 1 must lead naturally to the coupling of sigmoid transfer logic and Hebbian learning. Thus the author has coined the Lagrangian Constraint Neural Network (LCNN) since 1997. Nonlinear ICA generalization by LCNN and two conjugate gradient ascents of two mirror symmetric MaxEnt's are indicated.
R.A. Choudrey and S.J. Roberts
Flexible Bayesian Independent Component Analysis for Blind Source Separation
Independent Component Analysis (ICA) is an important tool for extracting structure from data. ICA is traditionally performed under a maximum likelihood scheme in a latent variable model and in the absence of noise. Although extensively utilised, maximum likelihood estimation has well known drawbacks such as overfitting and sensitivity to localmaxima. In this paper, we propose a Bayesian learning scheme using the variational paradigm to learn the parameters of the model, estimate the source densities, and –together with Automatic Relevance Determination (ARD)  to infer the number of latent dimensions. We illustrate our method by separating a noisy mixture of images, estimating the noise and correctly inferring the true number of sources.
Albert Bijaoui, Danielle Nuzillard
Smoothing and Adaptive Denoising for Blind Source Separation
Pixel unmixing of multispectral astronomical images was examined as a blind source separation of an instantaneous mixture. The capabilities of separation algorithms were tested on different simulatd images. The results showed that only in case of a high signalto noise ratio fine separations can be carried out. In this communication, the improvements resulting from a pre denoising are examined. Optimal linear smoothing and two adaptive wavelet denoisings were applied before separation. The increase of the separation quality of the obtained sources is discussed according to both the separation algorithms and the denoising methods.
Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, Benjamin Blankertz, Klaus Robert Muller
Nonlinear Blind Source Separation Using Kernel Feature Spaces
In this work we propose a kernelbased blind source separation (BSS) algorithm that can perform nonlinear BSS for general invertible nonlinearities. For our kTDSEP algorithm we have to go through four steps: (i) adapting to the intrinsic dimension of the data mapped to feature space F , (ii) finding an orthonormal basis of this submanifold, (iii) mapping the data into the subspace of F spanned by this orthonormal basis, and (iv) applying temporal decorrelation BSS (TDSEP) to the mapped data. After demixing we get a number of irrelevant components and the original sources. To find out which ones are the components of interest, we propose a criterion that allows to identify the original sources. The excellent performance of kTDSEP is demonstrated in experiments on nonlinearly mixed speech data.
J. Eriksson, A. Kankainen, V. Koivunen
Novel Characteristic Function Based Criteria for ICA
We introduce two nonparametric independent component analysis (ICA) criteria based on factorization of characteristic functions. This approach has potential to separate wide class of distributions because characteristic function always exists. A simple criterion allowing for efficient search of the separating matrix and a more advanced criterion possessing desirable consistency property are presented. These criteria may easily be used in orthogonal ICA algorithms. Separating matrix is estimated by establishing pairwise independence among the source signals. Theoretical characteristic functions used in the criteria are replaced by empirical ones. In the examples, the reliable performance of the methods is demonstrated using a variety of source distributions including skewed and heavytailed distributions.
Toshinao Akuzawa
New Fast Factorization Method for Multivariate Optimization and its Realization as ICA Algorithm
A new framework for multivariate optimization by criteria invariant under componentwise scaling is constructed. These problems are naturally considered as problems on the coset R^{x^{N}} \ GL (N,R). We show that there is a duality between the optimization flow on this coset and the dynamics of quantum lattice with inner degrees of freedom. Then we propose a new algorithm for optimization problems on this coset named nested Newton’s method, whose essence is the ignorance of nbody interactions with n≥3 if we explain it by using its analogy to quantum lattice. This method is readily applicable as a highly useful ICA algorithm, which is robust under gaussian noises, quite fast, and practical for large dimensional problems. The last feature comes from the fact that our method requires memory space of order N^{2}, whereas the conventional Newton’s method for ICA (and the JADE) requires that of order N^{4}. The matlab code for this algorithm is available from our website.
Wei Lu, Jagath C. Rajapakse
We present a novel approach to extract a subset of independent sources from multidimensional observations when some a priori information that can be incorporated to the learning algorithm as reference is available. The constrained independent component analysis (cICA) is extended to use new constraints, and a Newtonlike learning algorithm is proposed to give an optimal solution to the constrained optimization problem. The convergence and the effect of parameters of the learning algorithm are analyzed. Simulations with the mixtures of deterministic and random signals and synthetic fMRI data demonstrate the efficacy and accuracy of the proposed algorithm.
Kenneth E. Hild II, Deniz Erdogmus, Jose C. Principe
OnLine Minimum Mutual Information Method for TimeVarying Blind Source Separation
The MeRMaId (Minimum Renyi’s Mutual Information) algorithm for BSS (blind source separation) has previously been shown to outperform several popular algorithms in terms of data efficiency. The algorithms it compared favorably with include Hyvaerinen’s FastICA, Bell and Sejnowski’s Infomax, and Comon’s MMI (Minimum Mutual Information) methods. The drawback is that the MeRMaId algorithm has a computational complexity of O(L ^{2} ), as compared to O(L) for the other three. However, a new advancement referred to as SIG (Stochastic Information Gradient), can be used to modify the MeRMaId criterion such that the complexity is reduced to O(L). The modified criterion is then applied to the separation of instantaneously mixed sources using an online implementation. Simulations demonstrate that the new algorithm preserves the separation performance of the original algorithm and, in fact, compares quite favorably with several published methods.
Shoko Araki, Shoji Makino ,Ryo Mukai, Tsuyoki Nishikawa, Hiroshi Saruwatari
Fundamental Limitation of Frequency Domain Blind Source Separation for Convolved Mixture of Speech
Despite several recent proposals to achieve Blind Source Separation (BSS) for realistic acoustic signals, the separation performance is still not enough. In particular, when the length of an impulse response is long, the performance is highly limited. In this paper, we consider the reason for the p r performance of BSS in a long reverberation environment. First, we show that it is useless to be constrained by the condition P T, where T is the frame size f FFT and P is the length of a r m impulse response. We also discuss the limitation of frequency domain BSS, by showing that the frequency domain BSS framework is equivalent to two sets of frequency domain adaptive beamformers.
Massoud BabaieZadeh, Christian Jutten, Kambiz Nayebi
Blind Separating Convolutive Post NonLinear Mixtures
This paper addresses blind source separation in convolutive post nonlinear (CPNL) mixtures. In these mixtures, the sources are mixed convolutively, and then measured by nonlinear (e.g. saturated) sensors. The algorithm is based on minimizing the mutual information by using multivariate score functions.
Radu Balan, Justinian Rosca, Scott Rickard
Robustness of Parametric Source Demixing in Echoic Environments
Blind source separation (BSS) of audio signals in echoic environments such as an office room is still a very challenging problem. Here we approach the problem from a practical perspective and shed light on how robust a two channel echoic parametric demixing can get. We assume that an oracle (i.e. a perfect estimator) provides a truncated estimate of the mixing FIR filters for a given source configuration. This way we can study the properties of a parametric demixer using the adjoint of the truncated mixing matrix. For several degrees of truncation, we compute how the separation SNR varies as a function of the uncertainty of the true source position. The true source position is uniformly distributed within a sphere of radius R around an assumed position, to reflect the fact that parameters of interest are imprecisely estimated. Simulations of artificial echoic mixings show that the higher order demixing filters have little robustness to position uncertainties (and therefore to errors of estimation) while the overall performance remains almost constant beyond the second order approximation. This should represent a guideline for what is practically achievable with a class of BSS techniques in echoic environments.
Allan Kardec Barros, Noboru Ohnishi
Fetal Heart Rate Variability Extraction by Frequency Tracking
In this work, we propose an algorithm to extract the fetal heart rate variability from an ECG measured from the mother abdomen. The algorithm consists of two methods: a separation algorithm based on secondorder statistics that extracts the desired signal in one shot through the data, and a hearth instantaneous frequency (HIF) estimator. The HIF algorithm is used to extract the mother heart rate which serves as reference to extract the fetal heart rate. We carried out simulations where the signals overlap in frequency and time, and showed that the it worked efficiently.
V. Calhoun, T. Adali, G. Pearlson, J. Pekar
Group ICA of Functional MRI Data: Separability, Stationarity, and Inference
Independent component analysis (ICA) is being increasingly applied to functional MRI (fMRI) data. A principal advantage of this approach is its applicability to cognitive paradigms for which detailed a priori models of brain activity are not available. ICA has been successfully utilized to analyze singlesubject fMRI data sets, and we have recently extended this work to provide for group inferences. In order to perform group analysis, we concatenate the singlesubject images in time and perform a single ICA estimation, then backreconstruct individual subject maps and time courses. When applied to fMRI data acquired during a simple visual paradigm, our group ICA analysis revealed taskrelated components in left and right visual cortex, a transiently taskrelated component in bilateral occipital/parietal cortex, and a non taskrelated component in bilateral visual association cortex. In this work, we develop three important areas needed for applying ICA to group data: separability, stationarity, and inference. Our results further demonstrate the utility of using such a method for making group inferences on fMRI data using ICA.
LaiWan Chan, SiuMing Cha
Selection of Independent Factor Model in Finance
In finance, factor model is a fundamental model to describe the return generation process. Traditionally, the factors are assumed to be uncorrelated with each other. We argue that independence is a better assumption to factor model from the viewpoint of portfolio management. Based on this assumption, we propose the independent factor model. As the factors are independent, construction of the model would be another application of Independent Component Analysis (ICA) in finance. In this paper, we illustrate how we select the factors in the independent factor models. Securities in the Hong Kong market were used in the experiment. Minimum description length (MDL) was used to select the number of factors. We examine four sorting criteria for factor selection. The resultant models were crossexamined by the runs test.
Changkyu Choi
Speech Enhancement Using Sparse Code Shrinkage and Global Soft Decision
This paper relates to a method of enhancing speech quality by eliminating noise in speech presence intervals as well as in speech absence intervals based on speech absence probability. To determine the speech presence and absence intervals, we utilize the global soft decision. This decision makes the estimated statistical parameters of signal density models more reliable. Based on these parameters the noise suppressor equipped with sparse code shrinkage functions reduces noise considerably in realtime.
Andrzej Cichocki, Adel Belouchrani
Source Separation of Temporally Correlated Source Using Bank of Band Pass Filters
This paper introduces a new source separation algorithms exploiting the difference in the spectra shapes of the source signals. The proposed approach relies only on secondorder statistics and estimates the mixing matrix by using eigenvalue decomposition of covariance matrix of prewithened sensor signals or alternatively an input output identification procedure using as inputs linear band pass filtered versions of the estimated colored sources. An adaptive implementation of the proposed technique is presented. The new algorithm shows to be computationally very simple and efficient. In addition and in contrast to other existing techniques, the covariance of the noise do not need to be modeled. The effectiveness of the proposed method is illustrated by some numerical simulations.
Adriana Dapena, Monica F. Bugallo, Luis Castedo
Separation of Convolutive Mixtures of TemporallyWhite Signals: A Novel FrequencyDomain Approach
In this paper we propose a novel approach for separating convolutive mixtures in the frequency domain. This approach involves the solution of several instantaneous mixing problems and the elimination of the indeterminacies which appear because the sources may be extracted in a different order or with different amplitudes in some frequency bins. In order to separate each instantaneous mixture, we will extend the criterion proposed in [4]. We also show that both the permutation and the amplitude indeterminacies can be removed using secondorder statistics when the sources are temporallywhite.
Akira Date
An Information Theoretic Analysis of 256Channel EEG Recordings: MutualInformation and Measurement Selection Problem
How does one part affect another in the brain? How much information can we extract from the brain data? The multichannel EEG recording system is now available to study this issue. We recorded 256channel EEGs while a subject performed a visual discrimination task, and obtained mutual information between a visual stimulus condition and signals from single and multiple EEGs. Here we report preliminary results which show a power of the 256 channel recording system. In particular, we show examples that the best two informative independent measurements are not the two best.
Deniz Erdogmus, Luis Vielva, Jose Principe
Nonparametric Estimation and Tracking of the Mixing Matrix for Underdetermined Blind Source Separation
Blind source separation deals with the problem of estimating n source signals from m measurements, which are generated through an unknown mixing process. In the underdetermined linear case, where the number of measurements is smaller than the number of sources, the solution can be obtained in three stages: find a sparse representation domain for the signals, find the mixing matrix, and estimate the sources using the previous knowledge. This paper addresses the second stage. A nonparametric maximumlikelihood approach based on Parzen windowing is presented. It is shown that the peak points in the probability distribution of measurements directions correspond to the directions of the column vectors of the mixing matrix. An algorithm to estimate the column vectors in the static case, and to track the column vectors in the dynamic case is presented. The tracking capability of the algorithm is determined and, using a simple wave propagation model, corresponding limitations on the speeds of mobile sources are derived.
Simone Fiori
Some Properties of BellSejnowski PDFMatching Neuron
The aim of the present paper is to investigate the behavior of a singleinput singleunit system, learning through the maximumentropy principle, in order to understand some formal property of BellSejnowski’s PDFmatching neuron. The general learning equations are presented and two casestudy are discussed with details.
V. V. Gavrik
Criteria for a Linear Structure of Variance and Obtaining the Process Functions from Principal Components
The description of multivariate data with principal components allows most accurately to approximate a random function with a given number of expansion terms. The question is how to establish that the biorthogonal expansion is really finite in the physical sense and an experimental function is a random linear combination of several nonrandom functions over the instrumental error. Many situations are expected to result in the linear variance structure or be reducible to it on the base of physical considerations. Statistical criteria have been elaborated to detect the situations since a data variance could not be directly seen to possess the linear structure even in twodimensional situations. Some analytical properties of principal components are shown to give reliable rotation criteria for calculation the informal process functions. The approach is illustrated with the variancelinearization and rotation transforms for large sets of experimental dependencies describing the leaplike changes in the yield of a chemical process at the atombyatom growth of catalyst nanoclusters. Facing the latest results on the neural algorithms of identification and decisionmaking, the approach appears to promise efficiently to decode the large arrays of data on the electrical activities of brain.
Michel Haritopoulos, Hujun Yin, Nigel M. Allinson
Multiplicative Noise Removal Using SelfOrganizing Maps
This paper approaches the problem of image denoising from an Independent Component Analysis (ICA) perspective. Considering that the pixels intensity constituting the crude images represents the useful signal corrupted with noise, we show that, a nonlinear ICAbased approach can provide a satisfactory solution to the NonLinear Blind Source Separation problem (NLBSS). SelfOrganizing Maps (SOMs) are well suited for performing this task, due to their nonlinear mapping property. Separation results obtained from test images demonstrate the feasibility of the proposed method.
Robert Jenssen, Tor Arne Oigš ard, Torbjorn Eltoft and Alfred Hanssen
Sparse Code Shrinkage Based on the Normal Inverse Gaussian Density Model
In this paper we introduce the recent normal inverse Gaussian (NIG) probability density as a new model for sparsely coded data. The NIG density is a flexible, fourparameter density, which is highly suitable for modeling unimodal superGaussian data. We demonstrate that the NIG density provides a very good fit to the sparsely coded data, obtained here via an independent component analysis (ICA) transform of the observations. In image denoising, we utilize this new density by developing a NIGbased maximum a posteriori estimator of a sparsely coded image corrupted by white Gaussian noise. The estimator acts as a shrinkage operator on the noisy components in the sparse domain. We demonstrate the technique by an image denoising experiment.
Julia Karvanen, Visa Koivunen
Blind Separation Using Absolute Moments Based Adaptive Estimating Function
We propose new absolute moment based estimating functions for blind source separation purposes. Absolute moments are a computationally simple choice that can also adapt to the skewness of source distributions. They have lower sample variance than cumulants employed in many widely used ICA (Independent Component Analysis) methods. The complete estimating function consists of two parts that are sensitive to peakedness and asymmetry of the distribution, respectively. Expression for optimal weighting between the parts is derived using an efficacy measure. The performance of the proposed contrast and employed efficacy measure are studied in simulations.
Peter Meinicke, Helge Ritter
Independent Component Analysis with Quantizing Density Estimators
We propose an approach to source adaptivity in ICA based on quantizing density estimators (QDE). These estimators allow torealize source adaptivity in an efficient and nonparametric way and we show how their application can be viewed as a natural extension to recent approaches based on parametric models. In simulations we show that ICA based on QDE can considerably increase the performance of blind source separation as compared with flexible parametric approaches.
Ryo Mukai, Shoko Araki, Shoji Makino
Separation and Dereverberation Performance of Frequency Domain Blind Source Separation
In this paper, we investigate the separation and dereverberation performance of frequency domain Blind Source Separation (BSS) based on Independent Component Analysis (ICA) by measuring impulse responses of a system. Since ICA is a statistical method, i.e., it only attempts to make outputs independent, it is not easy to predict what is going on in a BSS system physically. We therefore investigate the detailed components in the processed signals of a whole BSS system from a physical and acoustical viewpoint. In particular, we focus on the direct sound and reverberation in the target and jammer signals. As a result, we reveal that the direct sound of a jammer can be removed and the reverberation of the jammer can be reduced to some degree by BSS, while the reverberation of the target cannot be reduced. Moreover, we show that a long frame length causes preecho noise, and this damages the quality of the separated signal.
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Satoshi Nakashima, Kiyotoshi Matsuoka
An Efficient Algorithm for Adaptive Separation of Mixture of Speech Signals
This paper proposes an efficient algorithm for blind source separation (BSS) of mixture of speech signals. Conventional online algorithms for blind separation usually assume that the sources are iid or linear processes. Since however speech signals have strong nonlinearity, those algorithms are not efficient with respect to convergence and sometimes induce instability. In order to solve these issues we introduce a more suitable probabilistic model for speech signals, namely, a speech signal is modeled as an amplitude modulation of a stationary random process. Based on the model, a new BSS algorithm is derived. A couple of examples reveal that the proposed algorithm determines a desired separator within a considerably short time.
Kamran Rahbar, James P. Reilly
Blind Source Separation Algorithm for MIMO Convolutive Mixtures
We consider the problem of blind source separation of MIMO convolutive mixtures for the general case where the number of sensors are greater than or equal to the number of sources. We assume that sources are nonstationary signals. The separation is performed in the frequency domain by joint minimization of the offdiagonal elements of observed signal's crossspectral density matrices over different epochs. We propose an efficient Newtonbased algorithm over the complex Stiefel manifold to minimize an appropriate cost function. We resolve the permutation problem using a novel tree structured diadic detection scheme. We find and correct wrong permutations at each frequency bin based on cross frequency correlation between diagonal elements of the output cross spectral matrices. We demonstrate the performance of the new algorithm using synthetic mixtures and real word recordings. The method has the additional advantage of fast convergence.
Fathi M. Salam, Khurram Waheed
State Space Feedforward and Feedback Structures for Blind Source Recovery
This paper presents two separate structures for the blind source recovery (BSR) of stochastically independent signal sources. We hypothesize linear state space models for both the mixing environment and the demixing (i.e. recovering) adaptive network. Separate algorithms for adaptive estimation of parameters for the feedforward and feedback recovering networks have been derived. Auxillay conditions for the convergence of these algorithms have also been derived and discussed. Simulation examples have been included to compare the results for both algorithms for an IIR mixing environment. Conclusive remarks about effectiveness of these techniques in various practical problems have also been included.
Mirko Solazzi, Raffaele Parisi, Aurelio Uncini
Blind Source Separation in Nonlinear Mixtures by Adaptive Spline Neural Networks
In this paper a novel paradigm for blind source separation in the presence of nonlinear mixtures is presented and described. The proposed approach employs a neural model based on adaptive Bspline functions. Signal separation is achieved through an information maximization criterion. Experimental results and comparison with existing solutions confirm the effectiveness of the proposed architecture.
Milutin Stanacevic, Marc Cohen, Gert Cauwenberghs
Blind Separation of Linear Convolutive Mixtures Using Orthogonal Filter Banks
We propose an algorithm and architecture for realtime blind source separation of linear convolutive mixtures using orthogonal filter banks. The adaptive algorithm derives from stochastic gradient descent optimization of a performance metric that quantifies independence not only across the reconstructed sources, but also across time within each source. The special case of a Laguerre section offers a compact representation with a small number of filter taps even under severe reverberant conditions, facilitating realtime implementation in a modular and scalable parallel architecture. Simulations of the proposed architecture and update rule validate the approach.
Kunio Takaya, KyungYung Choi
Detection of Facial Components in a Video Sequence by Independent Component Analysis
This paper presents two approaches for detecting facial components in the images contained in a video sequence by Independent Component Analysis (ICA). The ultimate objective is to map detected facial components such as eyes and mouth to a 3D wireframe model to be used in facial animation. One approach is to use face localization technique whereas the other deals with an entire image without cropping face part, but ßltering with wavelet subband ßlters. Face localization is achieved by using the human skin color ßltering in YCbCr subspace with other relevant facial information. The wavelet subband ßlter in the latter approach removes facial parts occupying a large area that contribute in ICA as large basis vectors. The method of Independent Component Analysis is then applied to identify main facial components for subsequent geometrical shape analysis.
Erik Visser, TeWon Lee, Manabu Otsuka
Speech Enhancement in a Noisy Car Environment
We present a new speech enhancement method for robust speech recognition in a noisy car environment. The method is based on the combination of two important building blocks, namely blind source separation given two microphone signals and speech denoising using a hybrid Wavelet  Independent Component Analysis (ICA) filterbank. The first block separates point sources such as the passenger’s voice signal whereas the second block eliminates distributed noise signals such as road and wind noise. We performed experiments with real recordings taken while driving in a noisy automobile environment. The method works nearly realtime and achieves good separation results.
Patrick M. Wong, Seungjin Choi, Yanping Niu
A Comparison of PCA/ICA for Data Preprocessing in a Geoscience Application
This paper presents a performance comparison of a variety of data preprocessing algorithms in a geoscience application. The selected algorithms are principal component analysis (PCA) and three different independent component analyses (FLEXICA, JADE and SOBI). These algorithms are applied to a set of electrical and radioactive signals obtained from a drilled well in Indonesia. Standard backpropagation neural networks are used to perform pattern (flow unit) classification from raw or preprocessed data. The results show that use of the preprocessed data gives more confident results than those obtained from the raw data. Among the preprocessing algorithms, FLEXICA seems to slightly outperform the others. The study also present a technological framework for combining results from different techniques and it shows that further improvement was achieved.
Liqing Zhang, Andrzej Cichocki
Sparse Representation and Blind Deconvolution of Dynamical Systems
In this paper, we discuss blind deconvolution of dynamical systems, described by the state space model. First we formulate blind deconvolution problem in the framework of the state space model. The blind deconvolution is fulfilled in two stages: internal representation and signal separation. We employ two different learning strategies for training the parameters in the two stages. A sparse representation approach is presented based on the independent decomposition. Some properties of the sparse representation approach are discussed. The natural gradient algorithm is used to train the external parameters in the stage of signal separation. The twostage approach provides a new insight into blind deconvolution in the statespace framework. Finally a computer simulation is given to show the validity and effectiveness of the statespace approach.
Michael Zibulevsky, Yehoshua Y. Zeevi
Source Extraction Using Sparse Representation
It was discovered recently that sparse decomposition by signal dictionaries results in dramatic improvement the qualities of blind source separation. We exploit sparse decomposition of a single souce in order to extract it from multidimensional sensor data, in applications where a rough template of the source is known. This leads to a convex optimization problem, which is solved by a Newtontype method. Complete and overcomplete dictionaries are considered. Simulations with synthetic evoked responses mixed into natural 122channel MEG data show significant improvement in accuracy of signal restoration.
Sophie Achard, Dinh Tuan Pham, Christian Jutten
Blind Source Separation in Post Nonlinear Mixtures
This work implements alternative algorithms to that of Taleb and Jutten for blind source separation in post nonlinear mixtures. We use the same mutual information criterion as them, but we exploit its invariance with respect to translation to express its relative gradient in terms of the derivatives of the nonlinear transformations. Then we develop algorithms based on these derivatives. In a semiparametric approach, the latter are parametrized by piecewise constant functions. All algorithms require only the estimation of the score functions of the reconstructed sources. A new method for score function estimation is presented for this purpose.
Frédéric Berthommier, Seungjin Choi
Evaluation of CASA and BSS Models for Subband CocktailParty Speech Separation
For speech segregation, a blind separation model (BSS) is tested together with a CASA model which is based on the localisation cue and the evaluation of the time delay of arrival (TDOA). The test database is composed of 332 binary mixture sentences recorded in stereo with a static setup. These are truncated at 1 second for the simulations. For applying the two models, we cut the frequency domain in a variable number of subbands, which are processed independently. Then, we evaluate the gain, using reference signals recorded in isolation. Without using this reference, a coherence index is also established for the BSS model, which measures the degree of convergence. After a careful analysis, we find gains of about 13dB for the two methods, which are smaller than those published for the same task. The variation of the number of subbands allows an optimisation, and we obtain a significant peak at 4 subbands for the CASA model, and a smaller maximum at 2 subbands for the BSS model.
J.D. Carew, V.M. Haughton, C.H. Moritz, B.P. Rogers, E.V. Nordheim, M.E. Meyerand
Frequency Domain Hybrid Independent Component Analysis of Functional Magnetic Resonance Imaging Data
Independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data reveals spatially independent patterns of functional activation. The purely datadriven approach of ICA makes statistical inference difficult. The purpose of this study was to develop a hybrid ICA in the frequency domain that enables statistical inference while preserving advantages of a datadriven ICA. Three normal volunteers were scanned with fMRI while they performed a working memory task. Their data were analyzed with frequency domain hybrid ICA. In each of the subjects, the patterns of activation corresponded to areas expected to be active during the fMRI task. This investigation demonstrates that a hybrid ICA in the frequency domain can statistically map functional activation while preserving the ability of ICA to blindly separate noise sources from the data.
Kai Chun Chiu, Lei Xu
Tests of Gaussian Temporal Factor Loadings in Financial APT
The main difficulty of financial APT analysis concerns identifying unambiguously the hidden statistical factors. Lack of effective techniques to retrieve the true factors often leads to inappropriate interpretation of the underlying factor structure. In literature, PCA and MLFA, assuming multivariate Gaussian distributions, and ICA, assuming nonGaussian distributions, are used to extract factors and determine the corresponding factor loadings. Recently, a new technique called TFA is proposed in [1, 2] which seeks to solve the problem of rotation indeterminacy encountered in conventional factor analysis. In this paper we will focus on statistical tests and inference on the APT temporal factor loadings recovered by TFA.
Seungjin Choi, Andrzej Cichocki, Yannick Deville
Differential Decorrelation for Nonstationary Source Separation
In this paper we consider the problem of source separation for the case that sources are (secondorder) nonstationary, especially their variances are slowly time varying. The differential correlation is exploited in order to capture the timevarying statistics of signals. We show that nonstationary source separation can be achieved by differential decorrelation. Algebraic methods are presented and discussed.
Simone Fiori, Pietro Burrascano
EctData Fusion by the Independent Component Analysis for NonDestructive Evaluation of Metallic Slabs
The aim of this paper is to present an application of ICA to nondestructive evaluation by unsupervised datafusion, which aims at discovering the flaws affecting a metallic slab. The signals acquired through an eddycurrent probe for nondestructive evaluation purposes are affected by strong noise and disturbances due to the mechanical system that the probe is mounted on. The availability of multiple measurements allows performing a linear datafusion which returns independent latent signals, one of which represents the flawrelated signal recovered from the noisy mixture. A oneunit neural ICA system is employed to extract such latent signal.
Pando Georgiev
Blind Source Separation of Bilinearly Mixed Signals
We propose a blind source separation model for statistically independent source signals, when the mixing operator is bilinear. This model is equivalent to a linear model for separation of pairwise multiplications the source signals. We prove that if the source signals are are colored and have distinct autocorrelation functions on a given set P, then we can extract simultaneously the pairwise multiplications of them, using a generalized eigenvalue problem.
Gen Hori, Masato Inoue, Shinichi Nishimura, Hiroyuki Nakahara
Blind Gene Classification Based on ICA of Microarray Data
The present study shows that an ICAbased method can, effectively and blindly, classify a vast amount of gene expression data into biologically meaningful groups. Specifically, we show (1) that genes, whose expression data are sampled at different times, can be classified into several groups, based on the correlation of each gene with independent component curves over time, and (2) that these classified groups by ICAbased method have a good match with the classified groups that are determined by use of domain knowledge and considered to be a benchmark. These results suggest that the ICAbased method can be a powerful approach to discover unknown gene functions.
Douglas R. Hundley, Michael J. Kirby, Markus G. Anderle
A Solution Procedure for Blind Signal Separation Using the Maximum Noise Fraction Approach: Algorithms and Examples
In this paper, we outline the relationship between the Maximum Noise Fraction (MNF) method–an algorithm first proposed for cleaning noise from multispectral image data and Blind Signal Separation (BSS). In particular we demonstrate under what conditions these methods are equivalent and indicate that MNF may be viewed as an extension to BSS for the case of subspace mixing. We present several examples and compare the results of the MNF method to algorithms for performing independent component analysis (ICA).
Mika Inki, Aapo Hyvaerinen
Two Methods for Estimating Overcomplete Independent Component Bases
Estimating overcomplete ICA bases is a difficult problem that emerges when using ICA on many kinds of natural data, e.g. image data. Most algorithms are based on approximations of the likelihood, which leads to computationally heavy procedures. Here we introduce two algorithms that are based on heuristic approximations and estimate an approximate overcomplete basis quite fast. The algorithms are based on quasiorthogonality in highdimensional spaces, and the gaussianization procedure, respectively.
Andreas Jung, Fabian J. Theis, Carlos G. Puntonet, Elmar W. Lang
Fastgeo – A Histogram Based Approach to Linear Geometric ICA
Guided by the principles of neural geometric ICA, we present a new approach to linear geometric ICA based on histograms rather than basis vectors. Considering that the learning process converges to the medians and not the maxima of the underlying distributions restricted to the receptive fields of the corresponding neurons, we observe a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost by a factor of 100 at least. We further explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix. Finally we discuss the problem of high dimensions and how it can be treated with geometrical ICA algorithms.
Martin Kermit, Oliver Tomic
Independent Components of Odour Signals
If two independent observations or processes are measured with the same apparatus, the inherent nature of the measuring device will in many cases introduce a dependency between the two recorded processes object to inspection. In this paper a suggestion of how Independent Component Analysis (ICA) can be used to identify such device dependencies and in turn give an estimated reconstruction of the observations without the correlation between signals introduced by the apparatus. The procedure is illustrated with the use of an "electronic nose" used to sample odours from mixtures of alcohol solutions. It is shown that ICA as a novel tool in the analysis of odour signals can extract the independent odour sources and give acceptable estimates of the ratio with which the alcohol solutions were mixed with two different approaches.
Mirko Knaak, Dieter Filbert
Acoustical SemiBlind Source Separation for Machine Monitoring
In this contribution, convolutive blind source separation algorithms are compared with the well studied theory of minimum variance beamforming. As a result, the equivalence between the delay vector in the PCA (principle component analysis) subspace and the column the of rotation matrix belonging to the target sound is shown. That equivalence yields a new semiblind algorithm being more robust than a minimum variance beamformer. The new algorithm is applied to the reconstruction of machine sounds (for classification purposes) when they are corrupted by strong interfering sources and a high noise level in a shop floor.
Mika Koganeyama, Hayaru Shouno, Toshyyasu Nagao, Kazuki Joe
Separation of Train Noise and Seismic Electric Signals from Telluric Current Data by ICA
Recently, detection of seismic electric signals (SESs) in telluric current data (TCD) observed using the VAN method has attracted notice for shortterm earthquake prediction. However, since most of the TCD collected in Japan is affected by train noise, detecting SESs in TCD itself is an extremely arduous job. The goal of this research is to derive a method for detecting SESs, which is difficult for VAN method experts because of train noise. We believe that SESs and train noise are independent signals. Therefore we attempted to apply Independent Component Analysis (ICA) to several TCD data sets which were measured at Matsushiro, Nagano. As a result, train noise and SESs were successfully separated using ICA.
Dorothea Kolossa, BertUwe Kohler, Markus Conrath, Reinhold Orglmeister
Optimal Permutation Correction by Multiobjective Genetic Algorithms
The separation of convolved signals can be performed in the frequency domain by splitting the signal into frequency bands, applying ICA techniques to each band and reassembling all bands to obtain the separated output signals. As ICA cannot guarantee for any ordering of output signals, the reassembly of the frequency bands must use some additional information in order to assign the frequency bands consistently to the right output. A number of different criteria have been proposed to solve this permutation problem. We have applied genetic algorithms at this point, which have the advantage of coping well with the discrete, multimodal search space that characterizes this problem. Furthermore, applying a multiobjective genetic algorithm allows to take more than one criterion for optimal separation into account simultaneously. This can give an insight into the relative merit of various criteria of separation optimality.
Russell H. Lambert, Marcel Joho, Heinz Mathis
Polynomial Singular Values for Number of Wideband Sources Estimation and Principal Component Analysis
A multipath enabled singular value decomposition (SVD) algorithm is presented, which will allow computation of wideband (polynomial) singular values, and hence, the signal+ noise and noise subspaces. Polynomial singular values are ordered according to total energy. The number of sources can be estimated using the scalar total energy values. Results using both simulated data on the computer and actual speech recorded in a noisy multipath environment are given to demonstrate the usefulness of the techniques shown. After number of sources estimation, only the signal+ noise subspace is used to create virtual sensors which have made optimal use of all the sensors. As a final signal copy step, standard blind independent component analysis (ICA) or blind source separation algorithms can be used to recover the original data from the virtual sensors. The number of estimated sources could also be given to a blind algorithm capable of using overdetermined sources and the algorithm can adaptively make use of all sensor data.
ShunTian Lou, XianDa Zhang
Blind Source Separation for Changing Source Number: A Neural Network Approach with a Variable Structure
Blind source separation (BSS) problems have recently become an active research area in both statistical signal processing and unsupervised neural learning. In most approaches, the number of source signals is typically assumed to be known a priori, but this does not usually hold in practical applications. Although the problem of determining the unknown source number has been studied recently, the BSS problem when the source number is changing dynamically is not yet considered. The main objective of this paper is to study and solve these two problems. Its basic idea is to utilize the correlation coefficients between output components of the neural network (NN) as a mean for determining the unknown source number and/or detecting dynamical change of the source number, and is to develop a neural network with variable structure to perform the corresponding adaptive blind source separation.
Ruben MartinClemente, Carlos G. Puntonet, Jose I. Acha
Blind Signal Separation Based on the Derivatives of the Output Cumulants and a Conjugate Gradient Algorithm
In this paper it is proven that the estimation of the separating system can be based on the cancellation of some second partial derivatives of the output crosscumulants. We propose a new contrast function that must be optimized on the Stiefel manifold. A conjugate gradient method is used in order to obtain a fast convergence speed.
HyungMin Park, SangHoon Oh, SooYoung Lee
On Adaptive Noise Canceling Based on Independent Component Analysis
We present a method to deal with adaptive noise canceling based on independent component analysis (ICA). Although popular leastmeansquares (LMS) algorithm removes noise components based on secondorder correlation, the proposed ICAbased algorithm can utilize higherorder statistics. Additionally, extending to transformdomain adaptive filtering (TDAF) methods, normalized ICAbased algorithm is derived to improve convergence rates. Experimental results show that the proposed ICAbased algorithm provides much better performances than conventional LMS approach in real world problems.
F.Rojas, I.Rojas , R.M.Clemente , C.G.Puntonet
Nonlinear Blind Source Separation Using Genetic Algorithms
This article proposes the fusion of two important paradigms, Genetic Algorithms and the Blind Separation of Sources (GABSS). Although the topic of BSS, by means of various techniques, including ICA, PCA and neural networks, has been amply discussed in the literature, to date the possibility of using genetic algorithms has not been explored. However, in nonlinear mixtures, optimisation of the system parameters and, especially, the search for invertible functions is very difficult by the existence of many local minima. From experimental results, this paper demonstrates the possible benefits offered by Gas I in combination with BSS, such as robustness against local minima, the parallel search for various solutions, and a high degree of flexibility in the evaluation function.
Justinian Rosca, NingPing Fan, Radu Balan
RealTime Audio Source Separation by Delay and Attenuation Compensation in the Time Domain
There is increased interest in using microphone arrays in a variety of audio source separation and consequently speech processing applications. In particular, small arrays of two to four microphones are presently under focus in the research literature, especially with regard to realtime source separation and speech enhancement capability. In this paper we focus on a realtime implementation of the delay and attenuation compensation (DAC) algorithm. Although the algorithm is designed for anechoic environments, its complexity and performance on real data represent a basis for designing more complex approaches to deal with reverberant environments. We highlight realtime issues and analyze the algorithm’s realtime performance on a database of more than 1000 mixtures of real voice recordings ranging from an anechoic to a strongly echoic office with reverberation time of 500 msec.
Hiroshi Saruwatari, Toshiya Kawamura, and Kiyohiro Shikano
Blind Source Separation Based on FastConvergence Algorithm Using ICA and Array Signal Processing
We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequencydomain ICA with directionofarrival (DOA) estimation, (2) null beamforming based on the estimated DOA, and (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast and highconvergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICAbased BSS method, even under reverberant conditions.
Fabian J. Theis, Andreas Jung, Elmar W. Lang, Carlos G. Puntonet
A Theoretic Model for Linear Geometric ICA
Geometric algorithms for linear ICA have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA has been proposed first by Puntonet and Prieto [1] [2] in order to separate linear mixtures. We will reconsider geometric ICA in a solid theoretic framework showing that fixpoints of geometric ICA fulfill a so called geometric convergence condition, which the mixed images of the unit vectors satisfy, too. This leads to a conjecture claiming that in the supergaussian unimodal symmetric case there is only one stable fixpoint, thus demonstrating uniqueness of geometric ICA after convergence.6
Ana Maria Tomé
An Iterative Eigendecomposition Approach to Blind Source Separation
In this work we address the generalized eigendecomposition approach (GED) to the blind source separation problem. We present an alternative formulation for GED based on the definition of congruent pencils. Making use of this definition, and matrix block operations, the eigendecompostion approach to blind source separation is completely characterized. We also present an iterative method to compute the eigendecomposition of a symmetric positive definite pencil.
Oliver Tomic, Martin Kermit
Discrimination and Interpretation of Electronic Nose Data Using ICA
This work reports on independent component analysis (ICA) as a tool used to discriminate between odour signals. Measurements of six different alcohol solutions were carried out with a commercial gas sensor array system, a so called electronic nose. The solutions were made of either pure propanol or butanol at concentration levels of 0.5%, 1% and 2%. Principal component analysis (PCA), a standard multivariate analysis tool for gas sensor data, needed three principal components (PC) for effective discrimination of the solutions. With ICA, only two independent components (IC) were needed to achieve a similar result. PC1 and IC1 gave both meaningful representations of alcohol concentrations in the solutions. However, only a combination of PC2 and PC3 could represent different types of alcohols as effectively as IC2 did.
Andreas Ziehe, Motoaki Kawanabe, Stefan Harmeling, KlausRobert Muller
Separation of PostNonlinear Mixtures Using Ace and Temporal Decorrelation
We propose an efficient method based on the concept of maximal correlation that reduces the postnonlinear blind source separation problem (PNL BSS) to a linear BSS problem. For this we apply the Alternating Conditional Expectation (ACE) algorithm – a powerful technique from nonparametric statistics – to approximately invert the (post)nonlinear functions. Interestingly, in the framework of the ACE method convergence can be proven and in the PNL BSS scenario the optimal transformation found by ACE will coincide with the desired inverse functions. After the nonlinearities have been removed by ACE, temporal decorrelation (TD) allows us to recover the source signals. An excellent performance underlines the validity of our approach and demonstrates the ACETD method on realistic examples.
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Pedro HojenSorensen, Lars Kai Hansen, Ole Winther
Mean Field Implementation of Bayesian ICA
In this contribution we review the mean field approach to Bayesian independent component analysis (ICA) recently developed by the authors [1, 2]. For the chosen setting of additive Gaussian noise on the measured signal and Maximum Likelihood II estimation of the mixing matrix and the noise, the expected sufficient statistics are obtained from the two first posterior moments of the sources. These can be effectively estimated using variational mean field theory and its linear response correction. We give an application to feature extraction in neuroimaging using a binary (stimuli/no stimuli) source paradigm. Finally, we discuss the possibilities of extending the framework to convolutive mixtures, temporal and ‘spatial’ source prior correlations, identification of common sources in mixtures of different media and ICA for density estimation.
Jianting Cao, Noboru Murata, Shunichi Amari, Andrzej Cichocki, Tsunehiro Takeda
A Robust ICA Approach for Unaveraged SingleTrial Auditory Evoked Fields Data Decomposition
Treating an averaged EFs (evokedfields) or ERPs (eventrelated potentials) data is a main approach in recent topics on applying ICA to neurobiological signal processing. By taking the average, the signalnoise ratio (SNR) is increased but some important information such as the strength of an evoked response and its dynamics will be lost. The singletrial data analysis, on the other hand, can avoid this problem but the poor SNR arises. In this paper, we present a robust approach for decomposing and localizing unaveraged singletrial MEGdata. Our approach has two procedures. In the first step, a PCAlike prewhitening with the highlevel noise reduction and an optimal dimensionality reduction techniques are presented. In the second step, a robust nonlinear function derived by the parameterized tdistribution model is applied to separate the mixtures of subGaussian and superGaussian source components. The results on unaveraged AEFs singletrial data analysis illustrate that not only the behavior and location but also the activity strength (amplitude) and dynamics of the individual evoked response can be visualized by using the proposed method.
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Jaakko Särelä, Harri Valpola, Ricardo Vigário, and Erkki Oja
Dynamical Factor Analysis of Rhythmic Magnetoencephalographic Activity
Dynamical factor analysis (DFA) is a generative dynamical algorithm, with linear mapping from factors to the observations and nonlinear mapping of the factor dynamics. The latter is modeled by a multilayer perceptron. Ensemble learning is used to estimate the DFA model in an unsupervised manner. The performance of the DFA have been tested in a set of artificially generated noisy modulated sinusoids. Furthermore, we have applied it to magnetoencephalographic data containing bursts of oscillatory brain activity. This paper shows that DFA can correctly estimate the underlying factors in both data sets.
A.Delorme, S. Makeig, T. Sejnowski
Automatic Artifact Rejection in EEG Using High Order Statistics and Independent Component Analysis
While it is now generally accepted that independent component analysis is a good tool for isolating both artifacts and cognitive related activations in EEG data, there is still little consensus about criteria for automatic rejection of artifactual components and single trials. Here we developed a graphical software to semiautomatically assist experimenter in rejecting independent components and noisy single data trials based on their statistical properties. We used kurtosis to detect peaky activity distributions that are characteristic of some types of artifact and entropy to detect unusual activity patterns. EEGLAB, a userfriendly graphic interface running under Matlab, allows the user to tune and calibrate the rejection criteria, to accept or override the suggested components and trials labeled for rejection, and to compare the results with other rejection methods.
Kevin H. Knuth, Wilson A. Truccolo, Steven L. Bressler, Mingzhou Ding
Separation of Multiple Evoked Responses using Differential Amplitude and Latency Variability
In neuroelectrophysiology one records electric potentials or magnetic fields generated by ensembles of synchronously active neurons in response to externally presented stimuli. These evoked responses are often produced by multiple generators in the presence of ongoing background activity. While source localization techniques or current source density estimation are usually used to identify generators, application of blind source separation techniques to obtain independent components has become more popular. We approach this problem by applying the Bayesian methodology to a more physiologicallyrealistic source model. As it is generally accepted that single trials vary in amplitude and latency, we incorporate this variability into the model. Rather than making the unrealistic assumption that these cortical components are independent of one another, our algorithm utilizes the differential amplitude and latency variability of the evoked waveforms to identify the cortical components. The algorithm is applied to intracorticallyrecorded local field potentials in monkeys performing a visuomotor task.
Jagath C. Rajapakse, Wei Lu
Extracting TaskRelated Components in Functional MRI
To extract consistently and transiently taskrelated component maps, a novel ICA paradigm, the ICA with reference (ICAR), is proposed. ICAR produces only component maps corresponding to the input stimuli which are used as reference signals in the learning paradigm, and all activations corresponding to a particular stimulus are located in a single component map. Computational and memory requirements of ICAR are much less than those required by spatial ICA or temporal ICA.
Irina F. Gorodnitsky , Adel Belouchrani
Joint Cumulant and Correlation Based Signal Separation with Application to EEG Data Analysis
Current methods in Blind Source Separation (BSS) utilize either the higher order statistics or the time delayed crosscorrelations to perform signal separation. In this paper we investigate a method for source separation which utilizes joint information from higher order statistics and delayed crosscorrelations. The algorithm is motivated by problems in analysis of Electroencephalography (EEG) data. We use an EEG analysis example to demonstrate that the Joint Cumulant and Correlation based (JCC) algorithm obtains better source separation than either of the group methods based on higher order statistics or time delayed cross correlations.
Diffusion Networks, Product of Experts, and Factor Analysis
Hinton (in press) recently proposed a learning algorithm called contrastive divergence learning for a class of probabilistic models called product of experts (PoE). Whereas in standard mixture models the “beliefs” of individual experts are averaged, in PoEs the “beliefs” are multiplied together and then renormalized. One advantage of this approach is that the combined beliefs can be much sharper than the individual beliefs of each expert. It has been shown that a restricted version of the Boltzmann machine, in which there are no lateral connections between hidden units or between observation units, is a PoE. In this paper we generalize these results to diffusion networks, a continuoustime, continuousstate version of the Boltzmann machine. We show that when the unit activation functions are linear, this PoE architecture is equivalent to a factor analyzer. This result suggests novel nonlinear generalizations of factor analysis and independent component analysis that could be implemented using interactive neural circuitry.
Laurent Giulieri, Nadège ThirionMoreau and PierreYves Arquès
Blind Source Separation Using Bilinear and Quadratic TimeFrequency Representations
We consider here the problem of blind sources separation. During the last decade, many solutions have been proposed among which contrasts functions, maximum likelihood functions, informationtheoretic criteria, etc... More recently, a new method based on some timefrequency (tf ) representations has been introduced by Belouchrani et al. It consists in jointdiagonalizing a combined set of “spatial tf distributions (stfd)” matrices. However, tf representations properties still not have been widely exploited to solve the sources separation problem. Our aim is to develop this point to take better advantage of bilinear and quadratic timefrequency representations properties. Hence, we derive new criteria of choice of stfd matrices sets to be jointdiagonalized and/or joint antidiagonalized. Finally, some computer simulations are presented in order to demonstrate the effectiveness of the proposed algorithm.
Kwokleung Chan, TeWon Lee, Terrence Sejnowski
Variational Learning of Clusters of Undercomplete Nonsymmetric Independent Components
We apply a variational method to automatically determine the number of mixtures of independent components in highdimensional datasets, in which the sources may be nonsymmetrically distributed. The data is modeled by clusters where each cluster is described as a linear mixing of independent factors. Because of the variational bayesian treatment, this method can yield an accurate density model for the observed data without overfitting problems. This allows us also to identify the dimensionality of the data for each cluster. The new method is applied to a difficult realworld medical dataset and is successful in diagnosing glaucoma.
Sepp Hochreiter, Michael C. Mozer
Monaural Separation and Classification of Mixed Signals: A SupportVector Regression Perspective
We address the problem of extracting multiple independent sources from a single mixture signal. Standard independentcomponent analysis approaches fail when the number of sources is greater than the number of mixtures. For this case, the sparsedecomposition method [1] has been proposed. The method relies on a dictionary of atomic signals and recovers the degree to which various dictionary atoms are present in the mixture. We show that the sparsedecomposition method is equivalent to a form of supportvector regression (SVR). The training inputs for the SVR are the dictionary atoms, and the corresponding targets are the dot product of the mixture and atom vectors. The SVR perspective provides a new interpretation of the sparsedecomposition method’s hyperparameter, and allows us to generalize and improve the method. The most important insight is that the sources do not have to be identical to dictionary atoms, but rather we can accommodate a manytoone mapping of source signals to dictionary atoms—a classification of sorts—characterized by a known nonlinear transformation with unknown parameters. The limitation of the SVR perspective is that it cannot recover the signal strength of an atom in the mixture; rather, it can only recover whether or not a particular atom was present. In experiments, we show that our model can handle difficult problems involving classification of sources. Our model may be particularly useful for speech signal processing and CDMAbased mobile communication, where in both cases we have knowledge about the invariances in the signal.
Pavel Kisilev, Michael Zibulevsky, Yehoshua Y. Zeevi, Barak A. Pearlmutter
Blind Source Separation via Multinode Sparse Representation
The blind source separation problem is concerned with extraction of the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. It was discovered recently, that exploiting the sparsity of sources in an appropriate representation according to some signal dictionary, dramatically improces the quality of separation. In this work we use the property of multiscale transforms, such as wavelet or wavelet packets, to decompose signals into sets of local features with various degrees of sparsity. We use this intrinsic property for selecting the best (most sparse) subsets of features for further separation. The performance of the algorithm is vertified on noisefree and noisy data. Experiments with simulated signals, musical sounds and images demonstrate significant improvement of separation quality over previously reported results.
Juan K. Lin
Lattice Decompositions of Multivariate Probability Density Functions Extending the ICA Model to Incorporate More General Source Structures and Dependencies
The classical ICA model assumes that observations are all linear combinations of statistically independent scalar sources. This, as well as prior assumptions on the number of sources and their distributions are often seen as the weakest aspects of the ICA source model. In this paper, we present the mathematical structure necessary for extending ICA to more flexible models of realworld data.
Mark Plumbley
Adaptive Lateral Inhibition for NonNegative ICA
We consider the problem of decomposing an observed input matrix (or vector sequence) X into the product of a mixing matrix W with a component matrix Y, i.e.X = WY, where (a) the elements of the mixing matrix and the component matrix are nonnegative, and (b) the underlying components are considered to be observations from an independent source. This is therefore a problem of nonnegative independent component analysis. Under certain reasonable conditions, it appears to be sufficient simply to ensure that the output matrix has diagonal covariance (in addition to the nonnegativity constraints) to find the independent basis. Neither higherorder statistics nor temporal correlations are required. The solution is implemented as a neural network with errorcorrecting forward/backward weights and linear antiHebbian lateral inhibition, and is demonstrated on small artificial data sets including a linear version of the Bars problem.
Arie Yeredor
Blind Source Separation with Pure Delay Mixtures
We address the problem of blind separation of mixtures consisting of pure unknown delays in addition to scalar mixing coefficients. Such a mixture is a hybrid situation resembling both static and convolutive mixtures, but essentially different from both: On one hand, staticmixture approaches cannot be readily applied in this context; On the other hand, conventional convolutivemixture approaches are not only over  parameterized for this problem, but are also incapable of accommodating fractional delays. We propose a secondorder statistics based algorithm, which uses a specially parameterized approximate joint diagonalization of spectral matrices to estimate the mixing coefficients as well as the delays. The joint diagonalization algorithm is an extension of the "ACDC" algorithm, previously proposed in the context of static mixtures. We provide analytic expressions for all minimization steps for the two sensors/ two sources case, and demonstrate the performance using simulations results.
J.R. Duann, T.P. Jung, W.J. Kuo, T.C. Yeh, S. Makeig, J.C. Hsieh, T. J. Sejnowski
Measuring the Variability of EventRelated Bold Signal
Most current analysis methods for functional magnetic resonance imaging (fMRI) data assume a priori knowledge of the time course of the hemodynamic response (HR) to experimental stimuli or events in brain areas of interest. In addition, they typically assume homogeneity of both the HR and the nonHR “noise” signals both across brain regions and across similar experimental events. When HRs vary unpredictably from area to area, or from trial to trial, different approaches are needed. Here we used infomax Independent Component Analysis (ICA) to detect and visualize variations in singletrial HRs in eventrelated fMRI data. ICA decomposition of the resulting BOLD data produced independent components with variable stimuluslocked HRs active in primary visual (V1) and medial temporal (MT/V5) cortices respectively. Contrary to expectation, in four of six subjects the HR of the V1 component contained two positive peaks in response to shortstimulus bursts, while nearly identical component maps were associated with singlepeaked HRs in longstimulus sessions from the same subject. Thus, ICA combined with singletrial visualization can reveal dramatic and unforeseen taskrelated HR variation not apparent to researchers analyzing the data with fixed HR templates.
Samer A. Abdallah, Mark D. Plumbley
If the Independent Components of Natural Images are Edges, What are the Independent Components of Natural Sounds?
Previous work has shown that various flavours of Independent Component Analysis, when applied to natural images, all result in broadly similar localised, oriented bandpass feature detectors, which have been likened to wavelets or edge detectors. In this paper, we present a similar analysis of ‘natural’ sounds drawn from two radio stations: one broadcasting mainly speech; the other mainly classical music. Many of the resulting basis vectors are quite waveletlike, and can easily be characterised in terms of their position and spread in the timefrequency plane. Some of them, however, particularly from the set trained on music, do not fit that interpretation very well. The WignerVille Distribution can be used to gain a clearer picture of timefrequency localization of these basis vectors. We conclude by suggesting that these results be compared with other widely used auditory representations such as shortterm Fourier transforms, wavelet transforms, and physiologically derived models based on the auditory filterbank.
Thomas Kolenda, Lars Kai Hansen, Jan Larsen
Signal Detection Using ICA: Application to Chat Room Topic Spotting
Signal detection and pattern recognition for online grouping huge amounts of data and retrospective analysis is becoming increasingly important as knowledge based standards, such as XML and advanced MPEG, gain popularity. Independent component analysis (ICA) can be used to both cluster and detect signals with weak a priori assumptions in multimedia contexts. ICA of real world data is typically performed without knowledge of the number of nontrivial independent components, hence, it is of interest to test hypotheses concerning the number of components or simply to test whether a given set of components is significant relative to a “white noise” null hypothesis. It was recently proposed to use the socalled Bayesian information criterion (BIC) approximation, for estimation of such probabilities of competing hypotheses. Here, we apply this approach to the understanding of chat. We show that ICA can detect meaningful context structures in a chat room log file.
Ella Bingham
Topic Identification in Dynamical Text by Extracting Minimum Complexity Time Components
The problem of analysing dynamically evolving textual data has recently arisen. An example of such data is the discussion appearing in Internet chat lines. In this paper a recently introduced source separation method, termed as complexity pursuit, is applied to the problem. The method is a generalisation of projection pursuit to time series and it is able to use both spatial and temporal dependency information in separating the topics of the discussion. Experimental results on chat line and newsgroup data demonstrate that the minimum complexity time series indeed do correspond to meaningful topics inherent in the dynamical text data, and also suggest the applicability of the method to querybased retrieval from a temporally changing text stream. The complexity pursuit method is compared to several ICAtype algorithms for time series.
Johan Himberg, Aapo Hyvaerinen
Independent Component Analysis for Binary Data: An Experimental Study
We consider a mixing model where independent binary components are mixed using binary OR operations. Using extensive simulations, we investigate whether the model can be estimated using ordinary cumulantbased ICA algorithms. We show that the model can indeed be estimated if the data is sparse enough. We also compare the 3^{rd} and 4the order cumulants. In the nonoise and lownoise cases, the 3^{rd} order cumulant performs better, but in the presence of strong noise, the 4^{th} –order cumulant, somewhat surprisingly, performs better for very sparse data.
YuHwan Kim, ByoungTak Zhang
Document Indexing Using Independent Topic Extraction
Text retrieval involves finding relevant information from a collection of documents given the user’s information need. Traditional information retrieval systems represent a document as a vector of words, where each component can be a simple word count or follows a more sophisticated weighting scheme. The composed matrix is usually sparse and some words are highly correlated with each other. Another representation scheme is focused on the underlying topics, which is usually obtained by a variety of dimension reduction techniques, where each document can be represented as a vector of topic intensity. In this paper, We proposed a novel indexing technique based on independent component analysis. From the experiments performed on AP news articles, the performance improvements is significant when the topic of query is closely related to the topics which is extracted from the ICA.
Wakako Hashimoto
Independent Component Analysis with Several Mixing Matrices
A new algorithm is proposed for the variation of independent component analysis (ICA) in which there are several mixing matrices and, for each set of independent components, one of the matrices is randomly chosen to mix the components. The algorithm utilizes highorder moments and can obtain consistent estimators even if the true probability density function of independent components is not obtained. The effectiveness of our algorithm is verified by a numerical experiment. This method can be used to analyze a class of data generated overcompletely, and to classify data in an unsupervised manner.
Adriana Dapena, Christine Serviere
A Simplified FrequencyDomain Approach for Blind Separation of Convolutive Mixtures
In the frequencydomain, a convolutive mixture can be interpreted as several instantaneous mixtures which may be separated using many existing algorithms. The main limitation of this approach is the large number of frequencies that must be considered. In addition, a permutation/amplitude correction must be performed when the sources are recovered in a different order or with different amplitudes in some frequency bins. In this paper we propose a novel approach for solving the convolutive problem using only two frequency bins. The idea deals with finding a 2 X 2 invertible matrix which relates the signals recovered in these frequency bins and the temporal sources. The existence of this matrix is due to use zeropadding for computing the Fourier transform of the observations. Several simulation results show the good performance of this simplified approach in different applications.
Simone Fiori, Pietro Burrascano
Electromagnetic Environmental Pollution Monitoring: Source Localization by the Independent Component Analysis
The aim of this paper is to present an electromagnetic source localization technique based on independent component analysis (ICA). Two ICA algorithms known from the literature, allowing to process complexvalued signals, are used to estimate the mixing operator from electromagnetic data; as the mixing operator contains important information about the source complex structure and about the electromagnetic field propagation phenomena, by properly interpreting the results given by the ICA algorithm it is possible to develop a blind source localization procedure. Performing such procedure is the first step in electromagnetic environmental pollution monitoring.
Pando Georgiev, Andrzej Cichocki
On Some Extensions of Natural Gradient Algorithm
Recently several novel gradient descent approaches like natural or relative gradient methods have been proposed to derive rigorously various powerful ICA algorithms. In this paper we propose some extensions of Amari’s Natural Gradient and AtickRedlich formulas. They allow us to derive rigorously some already known algorithms, like for example, robust ICA algorithm and local algorithm for blind decorrelation. Furthermore, we hope they enable us to generate the family of new algorithms with improved convergence speed or performance for various applications. We present conditions for which the proposed general gradient descent dynamical systems are stable. We show that the nonholonomic orthogonal algorithm can not be derived from minimization of any cost function. We propose a stabilized nonholonomic algorithm, which preserves the norm of the demixing matrix.
Shahram Hosseini, Christian Jutten, Dinh Tuan Pham
Blind Separation of Temporally Correlated Sources Using a Quasi Maximum Likelihood Approach
A quasimaximum likelihood approach is used for separating the instantaneous mixtures of temporally correlated, independent sources without either any preliminary transformation or a priori assumption about the probability distribution of the sources. A first order Markov model is used to represent the joint probability density of successive samples of each source. The joint probability density functions are estimated from the observations using a kernel method.
Jorge Igual, Andrés Camacho, Luis Vergara
Canceling Sinusoidal Interferences in Ultrasonic Applications with a BSS Algorithm for More Sources than Sensors
Sinusoidal interferences are found in ultrasonic signals when we try to characterize a material, as for example interferences coming from PC cards. We are interested in obtain a robust method that cancels these interferences preserving the waveform of the signal. A Blind Source Separation BSS method to extract these sinusoids is presented in this paper. We will get so many linear mixtures of the backscattering echo of the material and the sinusoids as we need from different pulse responses of the material.
GilJin Jang, TeWon Lee, YungHwan Oh [109]
Blind Separation of Single Channel Mixture Using ICA Basis Functions
A new technique has been developed to enable blind source separation given only a single channel recording. The proposed method infers source signals and their contribution factors at each time point by a number of adaptation steps maximizing loglikelihood of the estimated source parameters given the observed single channel data and sets of basis functions. This inferencing is possible due to the prior information on theinherent time structure of the sound sources by learning a priori sets of timedomain basis functions and the associated coeÆcient densities that encode the sources in a statistically efficient manner. A model for density estimation allows accurate modeling of the observation and our experimental results show close toperfect separation on simulated mixtures as well as recordings in a real environment employing mixtures of two different sources.
Inseon Jang, Seungjin Choi
Sequential Least Squares Algorithms for Blind CoChannel Signal Separation
In this paper we consider a problem of blind cochannel signal separation, the goal of which is to estimate multiple cochannel digitally modulated signals using an antenna array. We consider the joint maximum likelihood estimation [1] and present a sequential algorithm, which is referred to as sequential joint maximum likelihood (SJML) algorithm. In addition we also apply the sequential least squares to ILSP [2] and the resulting algorithm is referred to as the sequential least squares with projection (SLSP). Useful behavior of these two algorithms are confirmed by simulations.
M. Klajman, A.G. Constantinides [139]
A Combined Statistics Cost Function for Blind and SemiBlind Source Separation
Most Blind Source Separation algorithms separate the sources by using either second or higher order statistics. In this paper we suggest to use a weighted combination of the second order covariance matrices and the fourth order eigenmatrices to restore the original algorithms relying on a single type of statistic only, fail. We then develop a novel diagonalisation algorithm, the Cayley Joint Unitary Diagonalisation (CJUD) algorithm, to find the optimal unitary diagonaliser and to determine the weights. Except in some trivial cases, it is very hard to determine the weights without any prior information. We show in this paper how the use of some prior knowledge can be incorporated in the CJUD algorithm in order to get a better estimate of the weights. Simulations are presented to show the improvement in performance of the proposed algorithms.
Jos Koetsier, Donald MacDonald, Darryl Charles
Exploratory Correlation Analysis
We present a novel unsupervised artificial neural network for the extraction of common features in multiple data sources. This algorithm, which we name Exploratory Correlation Analysis (ECA), is a multistream extension of a neural implementation of Exploratory Projection Pursuit (EPP) and has a close relationship with Canonical Correlation Analysis (CCA). Whereas EPP identifies ”interesting” statistical directions in a single stream of data, ECA develops a joint coding of the common underlying statistical features across a number of data streams. It has been shown that the principle of contextual guidance may be used to find a sparse coding of the features in dual natural image patches that is very different from single stream sparse coding experiments. The network only identifies those features which exist in both data streams and thus tend to be fewer in number and more complex in nature.
Ivica Kopriva , Harold Szu
HuygensFresnel Principle Generates Nonlinear ICA Reducible to Solvable Incoherent Limit Linear ICA
Reticle trackers have been used successfully with a beam splitter for tracking and discrimination of several moving incoherent (heat) optical sources in the mathematical framework called Independent Component Analyses (ICA). Here we further explore the theoretical basis of the coherent and partially coherent illumination by laser for the possibility of blind source demixing. An application of the partial coherence theory and the HutgensFresnel principle is utilized to formulate the problem. When incoherence is assumed a linear ICA model is obtained while in most general case of either partially or totally coherent optical radiation the resulting signal model is inherently nonlinear. It can be transformed into linear one under very special condition that assumes no relative motion between the radiating sources. In the most general case of partially coherent radiation, tracking of the several moving optical sources by using the beam splitter based reticle trackers is possible either by using ICA algorithms developed for undercomplete representation or by introduction of one additional sensor.
Hervé Le Borgne, Anne GuérinDugué
SparseDispersed Coding and Images Discrimination with Independent Component Analysis
Independent Component Analysis applied to a set of natural images provides bandpassoriented filters, similar to simple cells of the primary visual cortex. We applied two types of preprocessing to the images, a lowpass and a whitening one in a multiresolution grid, and examine the properties of the detectors extracted by ICA. These detectors composed a new basis function set in which images are encoded. On one hand, the properties (sparseness and dispersal) of the resulting coding are compared for both preprocessing strategies. On the other hand, this new coding by independent features is used for discriminating natural images, that is a very challenging domain in image analysis and retrieval. We show that a criterion based on the dispersal property enhances the efficiency of the discrimination by selecting the most dispersed detectors coding the image database. This behaviour is well enhanced with whitened images.
Jae Sung Lee, Daniel D. Lee, Seugjin Choi, Dong Soo Lee
Application of NonNegative Matrix Factorization to Dynamic Positron Emission Tomography
Recently suggested nonnegative matrix factorization (NMF) seems to overcome fundamental limitations of factor analysis at least in theoretical aspect. NMF cost function uses Poisson statistics as a noise model, rather than the Gaussian statistics, and provides a simple learning rule, in contrast to the tricky optimization in factor analysis. To study the feasibility of NMF for the analysis of dynamic image sequences in nuclear medicine, NMF was applied to H2 15 O dynamic myocardial PET images acquired from dog studies, and the results were compared with those obtained by conventional factor analysis method. Using NMF we could obtain basis images corresponding to major cardiac components. Their timeactivity curves showed reasonable shapes that we have been familiar with. With the assumption of proper number of factors, NMF presented good results at least similar with those by factor analysis. Our results showed that NMF would be feasible for image segmentation and factor extraction from dynamic image sequences in nuclear medicine.
N. Mitianoudis, M. Davies
New FixedPoint ICA Algorithms for Convolved Mixtures
One of the most powerful techniques applied to blind audio source separation is Independent Component Analysis (ICA). For the separation of audio sources recorded in a real environment, we need to model the mixing process as convolutional. Many methods have been introduced for separating convolved mixtures, the most successful of which require working in the frequency domain [1], [2], [3], [4]. Most of these methods perform efficient separation of convolved mixtures, however they are relatively slow. The authors propose two fixedpoint algorithms for performing fast frequency domain ICA.
Satoshi Niijima, Shoogo Ueno
Universal Fourth Order Music Method: Incorporation of ICA into Meg Inverse Solution
In recent years, several inverse solutions of magnetoencephalography (MEG) have been proposed. Among them, the multiple signal classification (MUSIC) method utilizes spatiotemporal information obtained from magnetic fields. The conventional MUSIC method is, however, sensitive to Gaussian noise and a sufficiently large signaltonoise ratio (SNR) is required to estimate the number of sources and to specify the precise locations of electrical neural activities. In this paper, a universal fourth order MUSIC (UFOMUSIC) method, which is based on fourth order statistics, is proposed. This method is shown to be more robust against Gaussian noise than the conventional MUSIC method. It is an algebraic approach to independent component analysis (ICA). Although ICA and the analysis of the MEG inverse problem have been separately discussed, the proposed method incorporates ICA into the MEG inverse solution. The results of numerical simulations demonstrate the validity of the proposed method.
Danielle Nuzillard, Albert Bijaoui
Multiscale Contrasts for Blind Source Separation
The analysis of multispectral astronomical images was examined as a blind source separation (BSS) of an instantaneous mixture. The experimented BSS methods were based on different assumptions: i/the nonGaussianity measured by high order statistics (HOS), ii/ the correlation between shifted sources. A HOS approach taking into account the spatial organization is proposed from a decomposition in the wavelet space. A multiscale contrast taking into account the probability density function (PDF) at each scale, was first introduced. The resulting contrast provides few improvement in the separation. Thus a definition of the multiscale contrast which took into account a mask associated to a thresholding was examined. We show in this communication that this new statistical quantity provides an available criterion for BSS. .
Scott Rickard, Radu Balan, Justinian Rosca
RealTime TimeFrequency Based Blind Source Separation
We present a realtime version of the DUET algorithm for the blind separation of any number of sources using only two mixtures. The method applies when sources are Wdisjoint orthogonal, that is, when the supports of the windowed Fourier transform of any two signals in the mixture are disjoint sets, an assumption which is justified in the Appendix. The online algorithm is a Maximum Likelihood (ML) based gradient search method that is used to track the mixing parameters. The estimates of the mixing parameters are then used to partition the timefrequency representation of the mixtures to recover the original sources. The technique is valid even in the case when the number of sources is larger than the number of mixtures. The method was tested on mixtures generated from different voices and noises recorded from varying angles in both anechoic and echoic rooms. In total, over 1500 mixtures were tested. The average SNR gain of the demixing was 15 dB for anechoic room mixtures and 5 dB for echoic office mixtures. The algorithm runs 5 times faster than real time on a 750MHz laptop computer. Sample sound files can be found here: http://www.princeton.edu/˜srickard/bss.html
T.H. Sander, G. Wubbeler, L. Trahms, A. Lueschow, G. Curio
Identification of Visually Evoked Brain Activity and Cardiac Artifact Components through TimeDelayed Decorrelation
Applying the timedelayed decorrelation (TDD) algorithm to raw data from a visual stimulation magnetoencephalographic (MEG) experiment we investigate the viability of classification of components into artifact or stimulus related components. The TDD components associated with the cardiac artifact show a striking similarity with a Principal Component Analysis (PCA) of the averaged cardiac artifact. This could be due to a violation of the TDD assumptions by the cardiac artifact. Two TDD components have time series peaking consistently at the time expected for the primary response due to the visual stimulation, but their field maps are different from the earliest signal in the average response. An identification of TDD components with physiological sources needs further investigation.
Hiroshi Sawada, Ryo Mukai, Shoko Araki, Shoji Makino
A PolarCoordinate Based Activation Function for Frequency Domain Blind Source Separation
This paper presents a new activation function for an ICA algorithm to process complexvalued signals, which is used in frequency domain blind source separation. The new activation function is based on the polar coordinates of a complex number, whereas the conventional one is based on the Cartesian coordinates of a complex number and calculates the real part and imaginary part separately. The new activation function eliminates an undesirable constraint occurred by the conventional function. In experiments for separating speech signals in a reverberant environment, we obtained improved SNRs by using the new activation function.
Fabian J. Theis, Elmar W. Lang
Maximum Entropy and Minimal Mutual Information in a Nonlinear Model
In blind source separation, two different separation techniques are mainly used: Minimal Mutual Information (MMI), where minimization of the mutual output information yields an independent random vector, and Maximum Entropy (ME), where the output entropy is maximized. However, it is yet unclear why ME should solve the separation problem, ie. result in an independent vector. Amari has given a partial confirmation for ME in the linear case in [1], where he proves that under the assumption of vanishing expectancy of the sources ME does not change the solutions of MMI up to scaling and permutation.
In this paper, we generalize Amari’s approach to nonlinear ICA problems, where random vectors have been mixed by output functions of layered neural networks. We show that certain solution points of MMI are kept fixed by ME if no scaling of the weight vectors is allowed. In general, ME however might leave those MMI solutions using diagonal weights in the first network layer. Therefore, we conclude this paper by suggesting that in nonlinear ME algorithms diagonal weights should be fixed in later epochs.
Luis Vielva
Underdetermined Blind Source Separation Using a Probabilistic Source Sparsity Model
Blind source separation consists of recovering n source signals from m measurements that are an unknown function of the sources. In solving the underdetermined (m<n) linear problem three stages can be identified: to represent the signals in an appropriate domain, to estimate the mixing matrix, and to invert the linear problem to estimate the sources. As a consequence of having more degrees of freedom than constraints, the inverse problem has an infinite number of solutions. To choose the “best” solution, additional constraints have to be imposed on the basis of some performance criterion or previous knowledge. In this communication we present a method that choose the “best” demixing matrix in a sample by sample basis by using some previous knowledge of the statistics of the sources. The behaviour of the estimator is compared to the global pseudo inverse approach and with other local heuristic methods by means of Montecarlo simulations.
Ziyou Xiong, Thomas S. Huang
Nonlinear Independent Component Analysis (ICA) Using Power Series and Application to Blind Source Separation
Contribution of this paper is the derivation of an algorithm that generalizes Bell & Sejnowski’s classic ICA to tackle nonlinear ICA and the introduction of a new and efficient form of ”natural gradient”. This algorithm uses power series of nonlinear mixtures to approximate the Taylor expansion of the inverse function mapping from sources to mixtures. The approximation enables derivation of learning rules for weight matrix associated with power series of any order. When applied to blind source separation, it successfully separated nonlinear mixtures for which Bell & Sejnowski’s algorithm could not due to its linear mixture model. In separating linear mixtures using this algorithm, the weight matrices for higher order mixtures converge to zero matrix. This is consistent with intuition, suggesting the validity of the generalization.
Pierre Comon, Eric Moreau, Ludwig Rota
Blind Separation of Convolutive Mixtures: A ContrastBased Joint Diagonalization Approach
Blind Separation of convolutive mixtures and Blind Equalization of MultipleInput MultipleOutput (MIMO) channels are two different ways of naming the same problem, which we address here. The numerical algorithm, subsequently presented in detail, is based on theoretical result on contrasts recently published by the authors [1]. This algorithm consists of Partial Approximate Joint Diagonalization (PAJOD) of several matrices, containing some values of output cumulant multicorrelations.
M. Kawamoto, Y. Inouye, A. Mansour, and R.W. Liu
Blind Deconvolution Algorithms for MIMOFIR Systems Driven by FourthOrder Colored Signals
In this paper, we propose a new iterative algorithm to solve the blind deconvolution problem of MIMOFIR channels driven by source signals which are temporally secondorder uncorrelated but fourthorder correlated and spatially second and fourthorder uncorrelated. To achieve our goal, we extend the superexponential de ation algorithm proposed by Inouye and Tanebe [2] to the case of the blind deconvolution problem of MIMOFIR channels driven by the source signals which possess fourthorder autocorrelations. In our new approach, to recover one source signal, there are two stages: First, by using our proposed superexponential algorithm, a cascaded integratorcomb (CIC) filter is acquired. It implies that one filtered source signal is separated from the mixtures of the source signals. Next, by making the filtered source signal uncorrelated, one source signal is recovered from the filtered source signal. To show the validity of the proposed algorithm, some simulation results are presented.
Naoki Saito, Bertrand Benichou
The Spike Process: A Simple Test Case for Independent or Sparse Component Analysis
We examine curious behaviors of the Independent Component Analysis (ICA) and Sparse Component Analysis (SCA) when they are applied to some simple stochastic processes called the “simple” and “generalized” spike processes. Both processes put a single spike at a random location in the zero vector of length n for each realization. The simple spike process puts a unit impulse whereas the generalized spike process puts a sample from the standard normal distribution. We obtained interesting set of theorems for these processes. The behavior of SCA to these processes turned out to be much simpler than that of ICA. Our results are useful for validating any ICA/SCA software package because it is very easy to simulate these processes and the desirable answers are known from our theorems.
Alexandre Iline, Harri Valpola, Erkki Oja
Detecting Process State Changes by Nonlinear Blind Source Separation
A variant of nonlinear blind source separation, the Nonlinear Dynamic Factor Analysis (NDFA) model, is based on noisy nonlinear mixtures of state variables, which are controlled by nonlinear system dynamics. The problem setting is blind because both the state variables, the nonlinear mixing model, and the nonlinear dynamics are unknown. As a special problem we consider the ability of NDFA to detect abrupt changes in the process dynamics. It is shown experimentally that NDFA is highly accurate and outperforms several standard change detection methods in this task.
Harri Valpola, Tapani Raiko, Juha Karhunen
Building Blocks for Hierarchical Latent Variable Models
We introduce building blocks from which a large variety of latent variable models can be built. The blocks include continuous and discrete variables, summation, addition, nonlinearity and switching. Ensemble learning provides a cost function which can be used for updating the variables as well as optimising the model structure. The blocks are designed to fit together and to yield efficient update rules. Emphasis is on local computation which results in linear computational complexity. We propose and test a structure with a hierachical nonlinear model for variances and means.
Torbjorn Eltoft, Orjan Kristiansen
ICA and Nonlinear Time Series Prediction for Recovering Missing Data Segments in Multivariate Signals
In this paper we introduce a new method for filling in gaps in a time series belonging to a set of simultaneously recorded, statistically dependent signals. By combining the properties of the independent component analysis (ICA) transform with those of the dynamicalfunctional artificial neural network (DFANN), we have developed a predictor that effectively exploits the mutual dependency between the component signals. This is done by performing the predictions in the ICAdomain, whereas the prediction errors, which are used to update the model parameters, are calculated in the observation domain. We have shown that the ICA DFANN predictor is capable of accurately filling in gaps in both synthetic and real time series. Our tests show that the new approach outperforms a predictor based on a standard multilayer perceptron (MLP) network, and a predictor based on the finite impulse response (FIR) network.
Kiyotoshi Matsuoka, Satoshi Nakashima
Minimal Distortion Principle for Blind Source Separation
Blind source separation (BSS) is a method for recovering a set of source signals from the observation of their mixtures without any prior knowledge about the mixing process. In BSS the definition of a source signal has an inherent indeterminacy; any linear transform of a source signal can also be considered a source signal. Due to this indeterminacy, there are an infinite number of valid separators that can extract the source signals. This paper proposes a principle for choosing an optimal separator among them in a certain sense. The optimal choice is made such that the observed signals are the least subjected to distortion by the separator. The proposed normalization has some favorable features, particularly for BSS of convolutive mixture.
Tomasz Rutkowski, Andrzej Cichocki, Allan Kardec Barros
Speech Enhancement from Interfering Sounds Using CASA Techniques and Blind Source Separation
In this paper we propose novel biologically plausible model for segregation of one dominant speaker from the other concurrent speakers and environmental noise in real cocktailparty scenario. The developed method integrates two powerful techniques: computational scene analysis (CASA) and blind source separation (BSS) technique with bandpass preprocessing. Since each of these techniques applied alone has same limitations and drawbacks, we combine both methods in order to obtain improved performance. The computers simulations results show good performance for real room recordings, especially for the case where mixing convolutive (reverberant) system cannot be inverted by any of these method itself.
Frederic Abrard, Yannick Deville, Paul White
From Blind Source Separation to Blind Source Cancellation in the Underdetermined Case: A New Approach Based on TimeFrequency Analysis
Many source separation methods are restricted to nonGaussian, stationary and independent sources. This yields some problems in real applications where the sources often do not match these hypotheses. Moreover, in some cases we are dealing with more sources than available observations which is critical for most classical source separation approaches. In this paper, we propose a new simple source separation method which uses timefrequency information to cancel one source signal from two observations in linear instantaneous mixtures. This efficient method is directly designed for nonstationary sources and applies to various dependent or Gaussian signals which have different timefrequency representations. Its other attractive feature is that it performs source cancellation when the two considered mixtures contain more than two sources.
Detailed results concerning mixtures of speech and music signals are presented in this paper.
Sergio Cruces, Andrzej Cichocki, Shunichi Amari
Criteria for the Simultaneous Blind Extraction of Arbitrary Groups of Sources
This paper reviews several existing contrast functions for blind source extraction proposed in the areas of Projection Pursuit and Independent Component Analysis, in order to extend them to allow the simultaneous blind extraction of an arbitrary number of sources which is specified by user. Using these criteria a novel form of Amari’s extraction algorithm has been derived. The necessary and sufficient asymptotical stability conditions that we obtain for this algorithm help us to develop stepsizes that result in a fast convergence. Finally, we exhibit some exemplary simulations that validate our theoretical results and illustrate the excellent performance of the presented algorithms.