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# Joint separation of clusters : theory and experiments

 dc.contributor.author Pattarawit Polpinit en_US dc.date.accessioned 2015-01-12T10:39:56Z dc.date.available 2015-01-12T10:39:56Z dc.identifier.other AIT Thesis no.CS-03-32 en_US dc.identifier.uri http://www.cs.ait.ac.th/xmlui/handle/123456789/269 dc.description Pathum Thani, Thailand : Asian Institute of Technology, 2003 en_US dc.description 36 p. en_US dc.description.abstract In this study we investigate a measure of the so-called joint separation of clusters from both the experimental and the theoretical points of view. In the experimental part, we measure the joint separation of a finite set of planes F of cardinality n ∏ 2 in term of the minmax angle of vectors on the planes belonging to a given set. Minmax angle is defined as the largest angle μ such that, if n vectors are chosen, one each on the plane, then at least two of the vectors have an angle of at least μ between them. Since obtaining minmax angle for arbitrary finite sets of plane in R 3 seems hard, we restrict to planes bounding the faces of a regular polyhedron. An algorithm based on Hill Climbing and Lingo model is used in the search for minmax angle of regular polyhedron. In the theoretical part, we study the generation of minmax angle as a notion of joint separation . Given a set of points of various colors on the line, an interval is called color-spanning if it contains at least one point of each color. We present an efficient algorithm to solve a problem of finding the minimum color spanning interval. Furthermore a semi-dynamic and a fully- dynamic algorithm to maintain such interval are proposed. dc.relation.ispartof Thesis no. CS-03-32 en_US dc.relation.ispartof Asian Institute of Technology. Thesis no. CS-03-32 en_US dc.subject Cluster set theory en_US dc.subject Polyhedra en_US dc.title Joint separation of clusters : theory and experiments en_US dc.type Thesis en_US
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