Paper:
Language: English:

Pseudo Online Independent Component Analysis for Dynamical Mixing Using Gradient Optimization

Takahiro Haneda and Shuxue Ding

School of Computer Science and Engineering The University of Aizu, Tsuruga, Ikki-Machi, Aisu-Wakamatsu City, Fukushima 965-8580, Japan

Received: November 25, 2008

Accepted: February 18, 2009

Keywords: independent component analysis (ICA), blind source separation (BSS), non-Gaussianity, online processing, step size

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.3 pp. 275-282, 2009

Abstract

Many of the algorithms developed for independent component analysis (ICA) operate efficiently only in batch processing because they include ensemble expectation operations. The online ICA algorithm that we propose in this paper operates recursively on sequential finite lengthened input blocks for learning mixing parameters and for separating sources based on maximized non-Gaussianity of outputs. To enable the algorithm to work more efficiently in separating nonstationary sources and/or in dynamical mixing environments, we proposed an online estimation for the covariance matrix of input signals and an online optimization for the step size. The covariance matrix is used to calculate the whitening matrix and must be estimated appropriately for ICA processing to be efficient. Determining the step-size parameter in an online algorithm is critical to higher convergence and stability after convergence but is notoriously tiresome, especially if sources or/and the mixing environment are nonstationary. The online optimized step size we proposed is automatically optimized for suiting the powers in each block. Numerical experiments confirm that the online algorithm converges efficiently and separates sources appropriately.

Reference

[1] A. Hyvarinen, J. Karhunen, and E. Oja, “Independent Component Analysis,” John Wiley and Sons, 2001.

[2] A. Hyvarinen, “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis,” IEEE Trans. on Neural Networks, pp. 626-634, 1999.

[3] A. Hyvarinen and E. Oja, “Independent Component Analysis: Algorithms and Applications,” Neural Networks, pp.,411-430, 2000.

[4] S. Ding, “Independent Component Analysis Based on Learning Updating with Forms of Matrix Transformations and the Diagonalization Principle,” Proc. FCST'06, pp. 203-210, 2006.

[5] S. Ding, “Independent Component Analysis via Learning Updating Using a Form of Orthonormal Transformation Based on the Diagonalization Principle,” Int. Journal of Innovative Computing, Information and Control, Vol.3, No.5, pp. 1219-1235, 2007.

[6] S. Ding, J. Huang, D. Wei and A. Cichocki, “A Near Real-Time Approach for Convolutive Blind Source Separation,” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 2006.

[7] X. Guo, L. Wang, X. Wu and D. Zhang, “Dynamic Analysis of Motor Imagery EEG Using Kurtosis Based Independent Component Analysis,” Advances in Cognitive Neurodynamics ICCN 2007, pp. 381-385, Springer Netherlands, 2008.

[8] N. N. Schraudolph and X. Giannakopoulos, “Online Independent Component Analysis With Local Learning Rate Adaptation,” Advances in Neural Information Processing Systems 12, pp. 789-795, MIT press, 2000.

[9] X. Zhu, X. Zhang, and Y. Su, “A fast NPCA algorithm for online blind source separation,'' Neurocomputing, Vol.69, pp. 964-968, 2005.

[10] X. Zhu, J. Ye, and X. Zhang, “A fixed-point nonlinear PCA algorithm for blind source separation,” Neurocomputing, Vol.69, pp. 264-272, 2005.

[11] M. Kurita, “New Calculus,” Gakujutsu Tosho Shuppann-sha (in Japanese).

[12] S. Oishi, “Numerical Calculation by Using MATLAB,” Baifukan (in Japanese).

[13] D. Schobben, EVALUATION OF BLIND SIGNAL SEPARATION MEHTODS, Kluwer Academic Publishers, 2001.