Rate of Convergence of the FOCUSS Algorithm

被引：6

作者：

Xie, Kan ^{[1
]}

He, Zhaoshui ^{[2
,3
]}

Cichocki, Andrzej ^{[4
,5
,6
]}

Fang, Xiaozhao ^{[7
]}

机构：

[1] Guangdong Univ Technol, Sch Automat, Guangzhou 510006, Guangdong, Peoples R China

[2] Guangdong Univ Technol, Sch Automat, Guangdong Key Lab IoT Informat Proc, Guangzhou 510006, Guangdong, Peoples R China

[3] RIKEN Brain Sci Inst, Lab Adv Brain Signal Proc, Saitama 3510198, Japan

[4] RIKEN Brain Sci Inst, Lab Adv Brain Signal Proc, Saitama 3510198, Japan

[5] Polish Acad Sci, Inst Syst Res Sci, PL-00447 Warsaw, Poland

[6] Skolkovo Inst Sci & Technol, Moscow 143025, Russia

[7] Guangdong Univ Technol, Sch Comp, Guangzhou 510006, Guangdong, Peoples R China

来源：

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS | 2017年 / 28卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Convergence; focal underdetermined system solver (FOCUSS) algorithm; linear convergence; rate of convergence; superlinear convergence; REWEIGHTED LEAST-SQUARES; SPARSE REPRESENTATION; RECONSTRUCTION;

D O I：

10.1109/TNNLS.2016.2532358

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the l(p)-norm with p is an element of (0, 2) to measure the sparsity of solutions. In this paper, we give a systematical analysis on the rate of convergence of the FOCUSS algorithm with respect to p. (0, 2). We prove that the FOCUSS algorithm converges superlinearly for 0 < p < 1 and linearly for 1 <= p < 2 usually, but may superlinearly in some very special scenarios. In addition, we verify its rates of convergence with respect to p by numerical experiments.

引用

页码：1276 / 1289

页数：14

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