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Set‐theoretic adaptive filtering based on data‐driven sparsification
Author(s) -
Yukawa Masahiro,
Yamada Isao
Publication year - 2011
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1237
Subject(s) - metric (unit) , subgradient method , algorithm , convergence (economics) , projection (relational algebra) , computer science , subspace topology , filter (signal processing) , adaptive filter , mathematical optimization , krylov subspace , set (abstract data type) , mathematics , variable (mathematics) , iterative method , artificial intelligence , mathematical analysis , operations management , economics , computer vision , programming language , economic growth
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. Copyright © 2011 John Wiley & Sons, Ltd.