On the convergence of SIPEX: a simultaneous principal components extraction algorithm

We have previously proposed SIPEX as a fast-converging and accurate principal components algorithm (Erdogmus, D. et al., Proc. ICASSP´02, vol.1, p.1069-72, 2002; Proc. EUSIPCO´02, vol.2, p.335-8, 2002). Its superiority in terms of data efficiency and solution accuracy was demonstrated through Monte Carlo simulations. We focus on the convergence properties of the original gradient-based algorithm as well as two modified versions of SIPEX based on approximations to the Hessian matrix of the cost function. We provide practical bounds on the step sizes of these algorithms and compare their convergence properties.