Blind Source Separation Using Temporal Predictability

A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O (N3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, sub-gaussian, and gaussian probability density functions and on mixtures of voices and music.

[1]  J. Friedman.  Exploratory Projection Pursuit , 1987 .

[2]  Geoffrey E. Hinton,et al.  Self-organizing neural network that discovers surfaces in random-dot stereograms , 1992, Nature.

[3]  Suzanna Becker,et al.  Learning to Categorize Objects Using Temporal Coherence , 1992, NIPS.

[4]  Schuster,et al.  Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.

[5]  James V. Stone,et al.  A learning rule for extracting spatio-temporal invariances , 1995 .

[6]  Terrence J. Sejnowski,et al.  Blind separation and blind deconvolution: an information-theoretic approach , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  C. Lee Giles,et al.  Neural Information Processing Systems 7 , 1995 .

[8]  James V. Stone,et al.  A Canonical Microfunction for Learning Perceptual Invariances , 1996, Perception.

[9]  Barak A. Pearlmutter,et al.  A Context-Sensitive Generalization of ICA , 1996 .

[10]  S. Pincus,et al.  Randomness and degrees of irregularity. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[11]  James V. Stone.  Learning Perceptually Salient Visual Parameters Using Spatiotemporal Smoothness Constraints , 1996, Neural Computation.

[12]  James V. Stone,et al.  Unsupervised discovery of invariances , 1997 .

[13]  Hans Knutsson,et al.  Learning multidimensional signal processing , 1998, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[14]  Pierre Comon,et al.  Blind source separation: models, concepts, algorithms and performance , 1999 .

[15]  J. Príncipe,et al.  A Gaussianity measure for blind source separation insensitive to the sign of kurtosis , 1999, Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468).

[16]  J. Porrill,et al.  Regularisation Using Spatiotemporal Independence and Predictability , 1999 .

[17]  John Porrill,et al.  Analysis of Optical Imaging Data Using Weak Models and ICA , 2000 .

[18]  M. Girolami,et al.  Advances in Independent Component Analysis , 2000, Perspectives in Neural Computing.

[19]  James V. Stone.  Blind deconvolution using temporal predictability , 2002, Neurocomputing.

[20]  Krzysztof Siwek,et al.  Non independent strategies for blind source separation in functional MRI , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[21]  Hans Knutsson,et al.  Exploratory fMRI Analysis by Autocorrelation Maximization , 2002, NeuroImage.

[22]  James V. Stone,et al.  Spatiotemporal Independent Component Analysis of Event-Related fMRI Data Using Skewed Probability Density Functions , 2002, NeuroImage.

[23]  James V. Stone.  Independent component analysis: an introduction , 2002, Trends in Cognitive Sciences.

[24]  Michael J. Kirby,et al.  Blind source separation using the maximum signal fraction approach , 2002, Signal Process..