Abstract
We present a set of gradient based orthogonal and non-orthogonal matrix joint diagonalization algorithms. Our approach is to use the geometry of matrix Lie groups to develop continuous-time flows for joint diagonalization and derive their discretized versions. We employ the developed methods to construct a class of Independent Component Analysis (ICA) algorithms based on non-orthogonal joint diagonalization. These algorithms pre-whiten or sphere the data but do not restrict the subsequent search for the (reduced) un-mixing matrix to orthogonal matrices, hence they make effective use of both second and higher order statistics.
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Afsari, B., Krishnaprasad, P.S. (2004). Some Gradient Based Joint Diagonalization Methods for ICA. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_56
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DOI: https://doi.org/10.1007/978-3-540-30110-3_56
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