Eigenvalue decomposition of a cumulant tensor with applications
Pierre Comon, J.-F. Cardoso · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
The so-called Independent Component Analysis (ICA) raises new numerical problems of particular nature. In fact contrary to the Principal Component Analysis (PCA) ICA requires the resorting to statistics of order higher than 2 involving necessarily objects with more than two indices such as the fourth-order cumulant tensor. ICA computation may be related to the diagonalization of the cumulant tensor with some particularities stemming from the symmetries it enjoys. Two algorithms are proposed. The first connects the problem to the computation of eigenpairs of an hermitian operator defmed on the space of square matrices. The second algorithm reduces the complexity by making use of the information redundancy inherent in the cumulant tensor its convergence properties are much alike those of the Jacobi algorithm for EVD calculation. Key words: Identification Cumulant Principal Component Independent Component Mixture Contrast