TY - GEN

T1 - Sparse representation and its applications in blind source separation

AU - Li, Yuanqing

AU - Cichocki, Andrzej

AU - Amari, Shun Ichi

AU - Shishkin, Sergei

AU - Cao, Jianting

AU - Gu, Fanji

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880728405&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84880728405

SN - 0262201526

SN - 9780262201520

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003

PB - Neural information processing systems foundation

T2 - 17th Annual Conference on Neural Information Processing Systems, NIPS 2003

Y2 - 8 December 2003 through 13 December 2003

ER -