Phase Locked Matrix Factorization

We present a novel approach to separate linearly mixed dependent sources that are phase-locked. The separation is done through a minimization problem involving three variables (the mixing matrix, the source time-dependent amplitudes, and their relative phases). Results obtained in toy data sets show that this algorithm is very fast, that it estimates the mixing matrix with remarkable precision even with considerable amounts of noise, and that the sources are also correctly estimated. We interpret these results as a “proof-of-concept” that this approach is valid and discuss the necessary improvements to deal with more general situations.

[1]  Andreas Ziehe,et al.  TDSEP { an e(cid:14)cient algorithm for blind separation using time structure , 1998 .

[2]  José M. Bioucas-Dias,et al.  Independent Phase Analysis: Separating Phase-Locked Subspaces , 2010, LVA/ICA.

[3]  W. Singer,et al.  Neural Synchrony in Brain Disorders: Relevance for Cognitive Dysfunctions and Pathophysiology , 2006, Neuron.

[4]  Steven H. Strogatz,et al.  Synchronization: A Universal Concept in Nonlinear Sciences , 2003 .

[5]  Sadri Hassani,et al.  Nonlinear Dynamics and Chaos , 2000 .

[6]  J. Palva,et al.  Phase Synchrony among Neuronal Oscillations in the Human Cortex , 2005, The Journal of Neuroscience.

[7]  José M. Bioucas-Dias,et al.  Source Separation and Clustering of Phase-Locked Subspaces , 2011, IEEE Transactions on Neural Networks.

[8]  José M. Bioucas-Dias,et al.  Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing , 2010, 2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing.

[9]  D. Tucker,et al.  EEG coherency. I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. , 1997, Electroencephalography and clinical neurophysiology.

[10]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[11]  Robert Oostenveld,et al.  Imaging the human motor system’s beta-band synchronization during isometric contraction , 2008, NeuroImage.

[12]  Erkki Oja,et al.  Independent component approach to the analysis of EEG and MEG recordings , 2000, IEEE Transactions on Biomedical Engineering.

[13]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[14]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[15]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[16]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[17]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[18]  José M. Bioucas-Dias,et al.  Phase Unwrapping via Graph Cuts , 2007, IEEE Trans. Image Process..

[19]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.