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. © Springer-Verlag Berlin Heidelberg 2009.
CITATION STYLE
Lahat, D., Cardoso, J. F., & Messer, H. (2009). Optimal performance of second-order multidimensional ICA. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5441, pp. 50–57). https://doi.org/10.1007/978-3-642-00599-2_7
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