Graph, clique and facet of boolean logical polytope

Kedong Yan () and Hong Seo Ryoo ()
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Kedong Yan: Nanjing University of Science and Technology
Hong Seo Ryoo: Korea University

Journal of Global Optimization, 2022, vol. 82, issue 4, No 14, 1015-1052

Abstract: Abstract Logical analysis of data (LAD) discovers useful knowledge from a set of data in the form of a Boolean pattern for classifying future data. Generating a pattern has been shown to be equivalent to solving a 0–1 multilinear program (MP). Thus, the success of LAD is tightly related to how efficiently practical instances of pattern generation MP’s can be solved. For a polyhedral relaxation of LAD pattern generation MP, this paper introduces a new notion of similarity among data that allows for simultaneously relaxing multiple terms of the objective function of MP into a single valid inequality for the Boolean MP polytope. Specifically, we present a framework for constructing three types of strong valid inequalities from cliques in multiple graph representations of data that collectively yield a tight polyhedral relaxation of MP. Furthermore, we specify conditions under which each type of the new inequalities defines a facet of the MP polytope. In comparison with methods from the literature, benefits of the new inequalities are validated through classification experiments with 8 public machine learning datasets.

Keywords: Logical analysis of data; 0–1 multilinear programming; Polyhedral relaxation; Multi-term relaxation; Graph; Clique; Boolean polytope; Facet (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-021-01107-x

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