Convergence study of a Bounded Component Analysis algorithm

• We analyse the convergence of a Bounded Component Analysis algorithm.
• A suitable set of coefficients determine the behaviour of the iterations.
• We propose practical step sizes to guarantee the stability and other conditions.
• We provide a modification to improve the algorithm in the presence of noise.
• To guarantee the stability, we use a step size usually slower than the N-R one.

This work presents the convergence study of a component analysis algorithm that is designed for extracting a source from a linear mixture of bounded sources. The algorithm implements the parsimonious criterion of finding the linear projection of observations whose convex support has the minimum normalised perimeter. In a noiseless situation, our stability analysis provides recommendations for setting the step size of the algorithm. These recommendations are designed to guarantee the global monotonic convergence to the source that is closest to the algorithm׳s initialisation (in a given sense) while at the same time maintaining a fast local convergence rate in the neighborhood of this solution. In the absence of noise, these theoretical results have been corroborated by means of computer simulations. Furthermore, we have shown that in noisy mixtures, the performance of the algorithms is improved by eliminating the bias that noise creates.