Strong valid inequalities for Boolean logical pattern generation

Kedong Yan; Hong Seo Ryoo

doi:10.1007/s10898-017-0512-2

Strong valid inequalities for Boolean logical pattern generation

Kedong Yan, Hong Seo Ryoo

School of Industrial Management Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.

Original language	English
Pages (from-to)	183-230
Number of pages	48
Journal	Journal of Global Optimization
Volume	69
Issue number	1
DOIs	https://doi.org/10.1007/s10898-017-0512-2
Publication status	Published - 2017 Sept 1

Keywords

0–1 linearization
0–1 multilinear programming
Boolean logic
Clique
Hypercube
Logical analysis of data
Pattern

ASJC Scopus subject areas

Business, Management and Accounting (miscellaneous)
Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10898-017-0512-2

Cite this

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abstract = "0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.",

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KW - 0–1 multilinear programming

KW - Boolean logic

KW - Clique

KW - Hypercube

KW - Logical analysis of data

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Strong valid inequalities for Boolean logical pattern generation

Abstract

Keywords

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