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A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

chapter
posted on 2011-01-01, 00:00 authored by Jiaojiao Jiang, H Zhang, Shui Yu
Least square problem with l1 regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l1-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l1-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l1-regularized algorithms.

History

Title of book

High performance networking, computing, and communication systems : second international conference, ICHCC 2011, Singapore, May 5-6, 2011, selected papers

Series

Communications in computer and information science ; 163

Chapter number

67

Pagination

476 - 483

Publisher

Springer-Verlag

Place of publication

Berlin, Germany

ISSN

1865-0929

eISSN

1865-0937

ISBN-13

9783642250026

ISBN-10

3642250025

Language

eng

Publication classification

B1 Book chapter

Copyright notice

2011, Springer-Verlag Berlin Heidelberg

Extent

84

Editor/Contributor(s)

Y Wu