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2013 IEEE 13th International Conference on Data Mining (2013)
Dallas, TX, USA USA
Dec. 7, 2013 to Dec. 10, 2013
ISSN: 1550-4786
pp: 797-806
Sparse clustering, which aims at finding a proper partition of extremely high dimensional data set with fewest relevant features, has been attracted more and more attention. Most researches model the problem through minimizing weighted feature contributions subject to a l_1 constraint. However, the l_0 constraint is the essential constraint for sparse modeling while the l_1 constraint is only a convex relaxation of it. In this article, we bridge the gap between the l_0 constraint and the l_1 constraint through development of two new sparse clustering models, which are the sparse k-means with the l_q(0 < q < 1) constraint and the sparse k-means with the l0 constraint. By proving the certain forms of the optimal solutiion of particular l_q(0 = q < 1) non-convex optimizations, two efficient iterative algorithms are proposed. We conclude with experiments on both synthetic data and the Allen Developing on both synthetic data and the l_q(0 = q < 1) models exhibit the advantages compared with the standard k-mans and sparse k-means with the l1 constraint.
Conferences, Data mining

Y. Wang, X. Chang, R. Li and Z. Xu, "Sparse K-Means with the l_q(0leq q< 1) Constraint for High-Dimensional Data Clustering," 2013 IEEE 13th International Conference on Data Mining(ICDM), Dallas, TX, USA USA, 2013, pp. 797-806.
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