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
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.
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