Block Jacobi-Type Methods for Log-Likelihood based Linear Independent Subspace Analysis

Independent subspace analysis (ISA) is a natural generalisation of independent component analysis (ICA) incorporated with invariant feature subspaces, where mutual statistical independence exists between subspaces, while mutual statistical dependence is still allowed between components within the same subspace. In this paper, we develop a general scheme of block Jacobi-type ISA methods which optimise a popular family of log-likelihood based ISA contrast functions. It turns out that block Jacobi-type ISA method is an efficient tool for both parametric and nonparametric approaches. Rigorous analysis regarding the local convergence properties is provided in a general sense. A concrete realisation of the block Jacobi-type ISA method, employing a Newton step strategy, is proposed and demonstrates its local quadratic convergence properties to a correct sub-space separation. Performance of the proposed algorithms is investigated by numerical experiments.