Mining the bilinear structure of data with approximate joint diagonalization

Approximate Joint Diagonalization of a matrix set can solve the linear Blind Source Separation problem. If the data possesses a bilinear structure, for example a spatio-temporal structure, transformations such as tensor decomposition can be applied. In this paper we show how the linear and bilinear joint diagonalization can be applied for extracting sources according to a composite model where some of the sources have a linear structure and other a bilinear structure. This is the case of Event Related Potentials (ERPs). The proposed model achieves higher performance in term of shape and robustness for the estimation of ERP sources in a Brain Computer Interface experiment.

[1]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[2]  Anke Meyer-Bäse,et al.  Spatiotemporal blind source separation using double-sided approximate joint diagonalization , 2005, 2005 13th European Signal Processing Conference.

[3]  J. Polich Updating P300: An integrative theory of P3a and P3b , 2007, Clinical Neurophysiology.

[4]  Christian Jutten,et al.  An Introduction to EEG Source Analysis with an Illustration of a Study on Error-Related Potentials , 2014 .

[5]  Eric Moreau,et al.  New self-adaptative algorithms for source separation based on contrast functions , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.

[6]  Marco Congedo,et al.  Spatio-temporal common pattern: A companion method for ERP analysis in the time domain , 2016, Journal of Neuroscience Methods.

[7]  M. S. Babtlett Smoothing Periodograms from Time-Series with Continuous Spectra , 1948, Nature.

[8]  Fabian J. Theis,et al.  On the use of joint diagonalization in blind signal processing , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[9]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .

[10]  24th European Signal Processing Conference, EUSIPCO 2016, Budapest, Hungary, August 29 - September 2, 2016 , 2016, European Signal Processing Conference.

[11]  Pierre Comon,et al.  Blind source separation of underdetermined mixtures of event-related sources , 2014, Signal Process..

[12]  Qiu-Hua Lin,et al.  Generalized Non-Orthogonal Joint Diagonalization With LU Decomposition and Successive Rotations , 2015, IEEE Transactions on Signal Processing.

[13]  Dinh-Tuan Pham,et al.  Approximate Joint Singular Value Decomposition of an Asymmetric Rectangular Matrix Set , 2011, IEEE Transactions on Signal Processing.

[14]  Eric Moreau,et al.  A Decoupled Jacobi-Like Algorithm for Non-Unitary Joint Diagonalization of Complex-Valued Matrices , 2014, IEEE Signal Processing Letters.

[15]  Christian Jutten,et al.  "Brain Invaders 2" : an open source Plug & Play multi-user BCI videogame , 2016 .

[16]  Christian Jutten,et al.  On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics , 2008, Clinical Neurophysiology.

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