subspace maximum margin clustering
In text mining, we are often confronted with very high dimensional data. Clustering with high dimensional data is a challenging problem due to the curse of dimensionality . In this paper, to address this problem, we propose an subspace maximum margin clustering (SMMC) method, which performs dimensionality reduction and maximum margin clustering simultaneously within a unified framework. We aim to learn a subspace, in which we try to find a cluster assignment of the data points, together with a hyperplane classifier, such that the resultant margin is maximized among all possible cluster assignments and all possible subspaces. The original problem is transformed from learning the subspace to learning a positive semi-definite matrix, in order to avoid tuning the dimensionality of the subspace. The transformed problem can be solved efficiently via cutting plane technique and constrained concave-convex procedure (CCCP). Since the sub-problem in each iteration of CCCP is joint convex, alternating minimization is adopted to obtain the global optimum. Experiments on benchmark data sets illustrate that the proposed method outperforms the state of the art clustering methods as well as many dimensionality reduction based clustering approaches.
maximum margin clustering dimensionality reduction cutting plane constrained concave-convex procedure