Optimal mathematical programming and variable neighborhood search for k-modes categorical data clustering

Abstract

The conventional k-modes algorithm and its variants have been extensively used for categorical data clustering. However, these algorithms have some drawbacks, e.g. they can be trapped into local optima and sensitive to initial clusters/modes. Our numerical experiments even showed that the k-modes algorithm cannot identify the optimal clustering results for some special datasets regardless the selection of the initial centers. In this paper, for small-sized datasets we developed an optimal programming approach based on integer linear programming (ILP) for k-modes clustering, which is independent to the initial solution;. For medium and large sized datasets, we developed a heuristic algorithm that implements iterative partial optimization in the ILP approach based on a framework of variable neighborhood search, known as IPO-ILP-VNS, to search for nearoptimal results with controlled computing time. Experiments on 38 datasets from the UCI site, including 27 synthesized small datasets and 11 known benchmark datasets, were carried out to test the proposed ILP approach and the IPO-ILP-VNS algorithm. The experiment results outperformed the conventional and all other existing enhanced k-modes algorithms in literature.

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