Pivot selection strategies in Jacobi joint block-diagonalization

Abstract

A common problem in independent component analysis after prewhitening is to optimize some contrast on the orthogonal or unitary group. A popular approach is to optimize the contrast only with respect to a single angle (Givens rotation) and to iterate this procedure. In this paper we discuss the choice of the sequence of rotations for such so-called Jacobi-based techniques, in the context of joint block-diagonalization (JBD). Indeed, extensive simulations with synthetic data, reported in the paper, illustrates the sensitiveness of this choice, as standard cyclic sweeps appear to often lead to non-optimal solutions. While not being able to guarantee convergence to an optimal solution, we propose a new schedule which, from empirical testing, considerably increases the chances to achieve global minimization of the criterion. We also point out the interest of initializing JBD with the output of joint diagonalization (JD), corroborating the idea that JD could in fact perform JBD up to permutations, as conjectured in previous works. © Springer-Verlag Berlin Heidelberg 2007.