Learning complex-valued latent filters with absolute cosine similarity

Abstract

We propose a new sparse coding technique based on the power mean of phase-invariant cosine distances. Our approach is a generalization of sparse filtering and K-hyperlines clustering. It offers a better sparsity enforcer than the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm ratio that is typically used in sparse filtering. At the same time, the proposed approach scales better than the clustering counterparts for high-dimensional input. Our algorithm fully exploits the prior information obtained by preprocessing the observed data with whitening via an efficient row-wise decoupling scheme. In our simulating experiments, the algorithm produces better estimates than previous approaches do. It yields better separation of live recorded speech mixtures as well.