Clustering on antimatroids and convex geometries
نویسندگان
چکیده
The clustering problem as a problem of set function optimization with constraints is considered. The behavior of quasi-concave functions on antimatroids and on convex geometries is investigated. The duality of these two set function optimizations is proved. The greedy type Chain algorithm, which allows to find an optimal cluster, both as the most distant group on antimatroids and as a dense cluster on convex geometries, is described. Key-Words: Quasi-concave function, antimatroid, convex geometry, cluster, greedy algorithm
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