AMICA : An Adaptive Mixture of Independent Component Analyzers with Shared Components

We derive an asymptotic Newton algorithm for Quasi Maximum Likelihood estimation of the ICA mixture model, using the ordinary gradient and Hessian. The probabilistic mixture framework can accommodate non-stationary environments and arbitrary source densities. We prove asymptotic stability when the source models match the true sources. An application to EEG segmentation is given.

[1]  Dinh-Tuan Pham,et al.  Mutual information approach to blind separation of stationary sources , 2002, IEEE Trans. Inf. Theory.

[2]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[3]  Zoubin Ghahramani,et al.  Variational Inference for Bayesian Mixtures of Factor Analysers , 1999, NIPS.

[4]  J. Palmer Variational and scale mixture representations of non -Gaussian densities for estimation in the Bayesian linear model: Sparse coding, independent component analysis, and minimum entropy segmentation , 2006 .

[5]  Kenneth Kreutz-Delgado,et al.  Super-Gaussian Mixture Source Model for ICA , 2006, ICA.

[6]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001 .

[7]  David J. C. MacKay,et al.  Comparison of Approximate Methods for Handling Hyperparameters , 1999, Neural Computation.

[8]  Philippe Garat,et al.  Blind separation of mixture of independent sources through a quasi-maximum likelihood approach , 1997, IEEE Trans. Signal Process..

[9]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[10]  Alexander M. Bronstein,et al.  Relative optimization for blind deconvolution , 2005, IEEE Transactions on Signal Processing.

[11]  Aapo Hyvärinen,et al.  Topographic Independent Component Analysis , 2001, Neural Computation.

[12]  Hagai Attias,et al.  A Variational Bayesian Framework for Graphical Models , 1999 .

[13]  Te-Won Lee,et al.  Blind Source Separation Exploiting Higher-Order Frequency Dependencies , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[14]  Terrence J. Sejnowski,et al.  ICA Mixture Models for Unsupervised Classification of Non-Gaussian Classes and Automatic Context Switching in Blind Signal Separation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Hagai Attias,et al.  Independent Factor Analysis , 1999, Neural Computation.

[16]  S. Amari,et al.  Multichannel blind separation and deconvolution of sources with arbitrary distributions , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[17]  Terrence J. Sejnowski,et al.  Variational Learning of Clusters of Undercomplete Nonsymmetric Independent Components , 2003, J. Mach. Learn. Res..

[18]  Andrzej Cichocki,et al.  Stability Analysis of Learning Algorithms for Blind Source Separation , 1997, Neural Networks.

[19]  Zoubin Ghahramani,et al.  A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.

[20]  Te-Won Lee,et al.  Multivariate Scale Mixture of Gaussians Modeling , 2006, ICA.

[21]  Stephen J. Roberts,et al.  Variational Mixture of Bayesian Independent Component Analyzers , 2003, Neural Computation.

[22]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[23]  Harri Lappalainen,et al.  Ensemble learning for independent component analysis , 1999 .

[24]  Neil D. Lawrence,et al.  Variational inference for Student-t models: Robust Bayesian interpolation and generalised component analysis , 2005, Neurocomputing.

[25]  Hagai Attias,et al.  Blind Source Separation and Deconvolution: The Dynamic Component Analysis Algorithm , 1998, Neural Computation.