Some Gradient Based Joint Diagonalization Methods for ICA

Abstract. We present a set of gradient based orthogonal and nonorthogonal 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.

• Type: Conference
• Year: 2004
• Where: ICA
• Authors: Bijan Afsari, Perinkulam S. Krishnaprasad
• Keywords: ICA 2004, Joint Diagonalization, Matrix Joint Diagonalization, Non-orthogonal Joint Diagonalization