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A Unified View of Adaptive Variable-Metric Projection Algorithms

Abstract

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.

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Correspondence to Masahiro Yukawa.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yukawa, M., Yamada, I. A Unified View of Adaptive Variable-Metric Projection Algorithms. EURASIP J. Adv. Signal Process. 2009, 589260 (2009). https://doi.org/10.1155/2009/589260

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Keywords

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