Set-theoretic adaptive filtering based on data-driven sparsification

In this article, we propose a fast and efficient algorithm named the adaptive parallel Krylov-metric projection algorithm. The proposed algorithm is derived from the variable-metric adaptive projected subgradient method, which has recently been presented as a unified analytic tool for various adaptive filtering algorithms. The proposed algorithm features parallel projection-in a variable-metric sense-onto multiple closed convex sets containing the optimal filter with high probability. The metric is designed based on (i) sparsification by means of a certain data-dependent Krylov subspace and (ii) maximal use of the obtained sparse structure for fast convergence. The numerical examples show the advantages of the proposed algorithm over the existing ones in stationary/nonstationary environments.