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Progress in Computing Applications(PCA)

Mining the Interval Pattern of the Biomedical Clusters using Greedy Algorithms
Alexey V Galatenko, Stepan A Nersisyan, Vera V Pankratieva
Lomonosov Moscow State University Leninskie gory 1, 119991 Moscow Russia
Abstract: Interval pattern concepts are a particular case of pattern structures. They can be used to clusterize rows of a numerical formal context (data matrix): two rows are close to each other if their entries at the corresponding positions fall within a given interval. The problem of mining interval pattern concepts has much in common with the known problem related to computational geometry: given a nite set of points in the Euclidean space, position a box of a given size in such a way that it encloses as many points as possible. This problem and its variations have been thoroughly studied in the case of a plane; however, the authors are not aware of the existence of algorithms which in a reasonable time produce an exact solution in the space of an arbitrary dimension. There exists an approximate greedy algorithm for solving this problem. It produces a solution with time which is linear in the number of points and polynomial in dimension. We apply a clustering approach based on that algorithm to the gene expression table from the dataset “The Cancer Cell Line Encyclopedia”. The resulting partition well agrees with a priori known biological factors.
Keywords: Interval Pattern Concepts, Clustering, Greedy Algorithm Mining the Interval Pattern of the Biomedical Clusters using Greedy Algorithms
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