TY - JOUR
T1 - Optimal performance of second-order multidimensional ICA
AU - Lahat, Dana
AU - Cardoso, Jean Francois
AU - Messer, Hagit
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Blind source separation
KW - Correlated sources
KW - Independent component analysis
KW - Joint block diagonalization
KW - Multidimensional components
KW - Performance analysis
UR - http://www.scopus.com/inward/record.url?scp=67149137770&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-00599-2_7
DO - 10.1007/978-3-642-00599-2_7
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AN - SCOPUS:67149137770
SN - 0302-9743
VL - 5441
SP - 50
EP - 57
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
T2 - 8th International Conference on Independent Component Analysis and Signal Separation, ICA 2009
Y2 - 15 March 2009 through 18 March 2009
ER -