NDLI: On Algorithms for a Binary-Real (max, X) Matrix Approximation Problem

Content Provider	IEEE Xplore Digital Library
Author	De Schutter, B. Schepers, J. Van Mechelen, I.
Copyright Year	2006
Description	Author affiliation: Delft Center for Syst. & Control, Delft Univ. of Technol. (De Schutter, B.)
Abstract	We consider algorithms to solve the problem of approximating a given matrix D with the (max, times) product of a binary (i.e., a 0-1) matrix S and a real matrix P: $min_{SP}parS$ odot P - Dpar, The norm to be used is the $l_{1},$ $l_{2},$ or $l_{infin}$ norm, and the (max, times) matrix product is constructed in the same way as the conventional matrix product, but with addition replaced by maximization. This approximation problem arises among others in data clustering applications where the maximal component instead of the sum of the components determines the final result. We propose several algorithms to address this problem. The binary-real (max, times) matrix approximation problem can be solved exactly using mixed-integer programming, but since this approach suffers from combinatorial explosion we also propose some alternative approaches based on alternating nonlinear optimization, and a method to obtain good initial solutions. We conclude with a simulation study in which the performance and optimality of the different algorithms are compared
Starting Page	5168
Ending Page	5173
File Size	265161
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377787
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation algorithms Matrix decomposition Least squares approximation Clustering algorithms Quadratic programming USA Councils Explosions Optimization methods Data analysis Information analysis
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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