A general approach to sparse basis selection: Majorization, concavity, and affine scaling

A general approach to sparse basis selection: Majorization, concavity, and affine scaling (1997)

Cached

Download Links

[dsp.ucsd.edu]

by K. Kreutz-Delgado , B. D. Rao

Venue:	IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY
Citations:	5 - 2 self

Versions

Version History

Metadata Version 3

User correction supplied by mph

Datum	Value	Source
TITLE	A general approach to sparse basis selection: Majorization, concavity, and affine scaling	INFERENCE
AUTHOR NAME	K. Kreutz-Delgado	user correction
AUTHOR AFFIL	Electrical and Computer Engineering Department; University of California, San Diego	user correction
AUTHOR ADDR	9500 Gilman Drive, Mail Code 0407; La Jolla, California 92093-0407	user correction
AUTHOR NAME	B. D. Rao	user correction
AUTHOR AFFIL	Electrical and Computer Engineering Department; University of California, San Diego	user correction
AUTHOR ADDR	9500 Gilman Drive, Mail Code 0407; La Jolla, California 92093-0407	user correction
ABSTRACT	Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schur-concave functions, which are the class of functions consistent with the so-called Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schur-concave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.	SVM HeaderParse 0.2
YEAR	1997	SVM HeaderParse 0.2
VENUE	IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY	user correction
VENUE TYPE	TECHREPORT	INFERENCE
TECH	Technical Report UCSD-CIE-97-7-1	INFERENCE
CITATIONS	82 found	ParsCit 1.0