On the minimum perimeter criterion for bounded component analysis

Bounded component analysis refers to a set of unsupervised techniques for the identification and recovery of underlying components of observations whose support has clear boundaries. This contribution is focused on the statistical justification and practical implementation of the minimum perimeter criterion, a bounded component analysis technique that can be used for the extraction of complex signals. In particular, with the help of the isoperimetric inequality, we reveal the link of the robust optimization of a statistical risk function with this criterion. We also address the difficulties for its optimization since, at the separation solutions, the criterion is non-differentiable. A reformulation of its optimization is shown to lead to a practical implementation that, for sources with clear boundaries, outperforms the normalized MSE performance of the state-of-the-art blind separation methods, being even close to the optimal performance of supervised methods.