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  • Research Article
  • Open Access

A Unified View of Adaptive Variable-Metric Projection Algorithms

EURASIP Journal on Advances in Signal Processing20092009:589260

  • Received: 24 June 2009
  • Accepted: 29 October 2009
  • Published:


We present a unified analytic tool named variable-metric adaptive projected subgradient method (V-APSM) that encompasses the important family of adaptive variable-metric projection algorithms. The family includes the transform-domain adaptive filter, the Newton-method-based adaptive filters such as quasi-Newton, the proportionate adaptive filter, and the Krylov-proportionate adaptive filter. We provide a rigorous analysis of V-APSM regarding several invaluable properties including monotone approximation, which indicates stable tracking capability, and convergence to an asymptotically optimal point. Small metric-fluctuations are the key assumption for the analysis. Numerical examples show (i) the robustness of V-APSM against violation of the assumption and (ii) the remarkable advantages over its constant-metric counterpart for colored and nonstationary inputs under noisy situations.


  • Information Technology
  • Analytic Tool
  • Quantum Information
  • Optimal Point
  • Full Article

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Authors’ Affiliations

Mathematical Neuroscience Laboratory, BSI, RIKEN, 2-1 Hirosawa, Wako Saitama, 351-0198, Japan
Department of Communications and Integrated Systems, Tokyo Institute of Technology, Meguro-ku Tokyo, 152-8552, Japan


© M. Yukawa and I. Yamada. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.