Show simple item record

dc.contributor.authorEkin, O.en_US
dc.contributor.authorHammer, P. L.en_US
dc.contributor.authorKogan, A.en_US
dc.date.accessioned2015-07-28T11:56:38Z
dc.date.available2015-07-28T11:56:38Z
dc.date.issued2000en_US
dc.identifier.issn0304-3975
dc.identifier.urihttp://hdl.handle.net/11693/11007
dc.description.abstractA Boolean function is called k-convex if for any pair x,y of its true points at Hamming distance at most k, every point "between" x and y is also true. Given a set of true points and a set of false points, the central question of Logical Analysis of Data is the study of those Boolean functions whose values agree with those of the given points. In this paper we examine data sets which admit k-convex Boolean extensions. We provide polynomial algorithms for finding a k-convex extension, if any, and for finding the maximum k for which a k-convex extension exists. We study the problem of uniqueness, and provide a polynomial algorithm for checking whether all k-convex extensions agree in a point outside the given data set. We estimate the number of k-convex Boolean functions, and show that for small k this number is doubly exponential. On the other hand, we also show that for large k the class of k-convex Boolean functions is PAC-learnable. (C) 2000 Elsevier Science B.V. All rights reserved.en_US
dc.language.isoEnglishen_US
dc.source.titleTheoretical Computer Scienceen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/S0304-3975(98)00337-5en_US
dc.subjectPartially-defined Boolean functionsen_US
dc.subjectOrthogonal disjunctive normal formsen_US
dc.subjectComputational learning theoryen_US
dc.subjectClassificationen_US
dc.subjectPolynomial algorithmsen_US
dc.titleConvexity and logical analysis of dataen_US
dc.typeArticleen_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.citation.spage95en_US
dc.citation.epage116en_US
dc.citation.volumeNumber244en_US
dc.citation.issueNumber2en_US
dc.identifier.doi10.1016/S0304-3975(98)00337-5en_US
dc.publisherElsevieren_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record