Combining blind source extraction with joint approximate diagonalization: Thin algorithms for ICA

Abstract

In this paper a multivariate contrast function is proposed for the blind signal extraction of a subset of the indepen dent components from a linear mixture. This contrast com bines the robustness of the joint approximate diagonaliza tion techniques with the flexibility of the methods for blind signal extraction. Its maximization leads to hierarchical and simultaneous ICA extraction algorithms which are respec tively based on the thin QR and thin SVD factorizations. The interesting similarities and differences with other exist ing contrasts and algorithms are commented.