A Fast Stochastic Gradient Algorithm: Maximal Use of Sparsification Benefits under Computational Constraints

Masahiro YUKAWA  Wolfgang UTSCHICK  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.2   pp.467-475
Publication Date: 2010/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.467
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
adaptive filter,  stochastic gradient algorithm,  proportionate adaptive filtering,  

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Summary: 
In this paper, we propose a novel stochastic gradient algorithm for efficient adaptive filtering. The basic idea is to sparsify the initial error vector and maximize the benefits from the sparsification under computational constraints. To this end, we formulate the task of algorithm-design as a constrained optimization problem and derive its (non-trivial) closed-form solution. The computational constraints are formed by focusing on the fact that the energy of the sparsified error vector concentrates at the first few components. The numerical examples demonstrate that the proposed algorithm achieves the convergence as fast as the computationally expensive method based on the optimization without the computational constraints.