Sparse representation and its applications in blind source separation

Yuanqing Li, Andrzej Cichocki, Shun Ichi Amari, Sergei Shishkin, Jianting Cao, Fanji Gu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Citations (Scopus)

Abstract

In this paper, sparse representation (factorization) of a data matrix is first discussed. An overcomplete basis matrix is estimated by using the K-means method. We have proved that for the estimated overcomplete basis matrix, the sparse solution (coefficient matrix) with minimum l1-norm is unique with probability of one, which can be obtained using a linear programming algorithm. The comparisons of the l1-norm solution and the l 0-norm solution are also presented, which can be used in recoverability analysis of blind source separation (BSS). Next, we apply the sparse matrix factorization approach to BSS in the overcomplete case. Generally, if the sources are not sufficiently sparse, we perform blind separation in the time-frequency domain after preprocessing the observed data using the wavelet packets transformation. Third, an EEG experimental data analysis example is presented to illustrate the usefulness of the proposed approach and demonstrate its performance. Two almost independent components obtained by the sparse representation method are selected for phase synchronization analysis, and their periods of significant phase synchronization are found which are related to tasks. Finally, concluding remarks review the approach and state areas that require further study.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003
PublisherNeural information processing systems foundation
ISBN (Print)0262201526, 9780262201520
Publication statusPublished - 2004
Externally publishedYes
Event17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada
Duration: 8 Dec 200313 Dec 2003

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Conference

Conference17th Annual Conference on Neural Information Processing Systems, NIPS 2003
Country/TerritoryCanada
CityVancouver, BC
Period8/12/0313/12/03

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