Masahiro Yukawa – Research Topics

Professor, Department of Electronics and Electrical Engineering, Keio University, JAPAN
Aim: Break the tradeoffs (in adaptive filtering algorithms) among
(1) Convergence/Tracking Capability
(2) Computational Complexity
(3) Robustness.

I have been working on the following two adaptive filtering paradigms:

  1. Krylov-Proportionate Adaptive Filtering
    Key: Sparsify the optimal filter by means of Krylov subspace
    [Basic Idea & Key References]

  2. Set-Theoretic Adaptive Filtering (established by Prof. Isao Yamada, my Ph.D. supervisor)
    (1) Characterize the optimal filter as a point in the intersection of multiple data-dependent closed convex sets.
    (2) Find a point in the intersection by iterative use of parallel subgradient projections.

  3. [My Contributions]

    The set-theoretic adaptive filtering is based on "Fixed Point Theory" and "Convex Functional Analysis"; the following are the key references:

      1. I. Yamada and K. Slavakis and K. Yamada, ``An efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques,'' IEEE Trans. Signal Processing, vol.50, no.5, pp. 1091--1101, May 2002.

      2. I. Yamada, ``Adaptive Projected Subgradient Method: A unified view for projection based adaptive algorithms,'' The Journal of IEICE, vol.86, no.8, pp. 654--658, August 2003 (in Japanese).

      3. I. Yamada and N. Ogura, ``Adaptive projected subgradient method for asymptotic minimization of sequence of nonnegative convex functions,'' Numerical Functional Analysis and Optimization, vol.25, no.7&8, pp. 593--617, 2004.

      4. Isao Yamada, Nobuhiko Ogura and Masahiro Yukawa, "Adaptive projected subgradient method and its acceleration techniques," in Proc. IFAC (International Federation of Automatic Control) Workshop on ALCOSP (Adaptation and Learning in Control and Signal Processing), TP4_A-1, pp. 639--644, Yokohama: Japan, Aug. 2004 (invited paper).

      5. K. Slavakis and I. Yamada and N. Ogura, ``Adaptive projected subgradient method over the fixed point set of strongly attracting non-expansive mappings,'' Numerical Functional Analysis and Optimization, vol.27, no.7&8, pp. 905--930, 2006.

      6. Isao Yamada, Konstantinos Slavakis, Masahiro Yukawa and Renato L. G. Cavalcante, "Adaptive projected subgradient method and its applications to robust signal processing," in Proc. IEEE ISCAS, pp. 269--272, Island of Kos: Greece, May 2006, (invited paper).