A unified view of adaptive variable-metric projection algorithms

Masahiro Yukawa, Isao Yamada

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


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.

Original languageEnglish
Article number589260
JournalEurasip Journal on Advances in Signal Processing
Publication statusPublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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