Optimal Performance of Second-Order Multidimensional ICA
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Independent component analysis (ICA) and blind source separation (BSS) deal with extracting mutually-independent elements from their observed mixtures. In “classical” ICA, each component is one-dimensional in the sense that it is proportional to a column of the mixing matrix. However, this paper considers a more general setup, of multidimensional components. In terms of the underlying sources, this means that the source covariance matrix is block-diagonal rather than diagonal, so that sources belonging to the same block are correlated whereas sources belonging to different blocks are uncorrelated. These two points of view —correlated sources vs. multidimensional components— are considered in this paper. The latter offers the benefit of providing a unique decomposition. We present a novel, closed-form expression for the optimal performance of second-order ICA in the case of multidimensional elements. Our analysis is verified through numerical experiments.
KeywordsIndependent component analysis blind source separation correlated sources multidimensional components performance analysis joint block diagonalization
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