Two applications of Min-Max-Jump distance

Gangli Liu

Keywords: distance, Silhouette coefficient, Davies–Bouldin index, Calinski-Harabasz index, K-means, clustering, clustering evaluation, minimax path problem

Abstract: We explore two applications of Min-Max-Jump distance (MMJ distance): MMJ-based K-means and MMJ-based internal clustering evaluation index. K-means and its variants are possibly the most popular clustering approach. A key drawback of K-means is that it cannot deal with data sets that are not the union of well-separated, spherical clusters. MMJ-based K-means proposed in this paper overcomes this demerit of K-means, so that it can handle irregularly shaped clusters. Evaluation (or "validation") of clustering results is fundamental to clustering and thus to machine learning. Popular internal clustering evaluation indices like Silhouette coefficient, Davies–Bouldin index, and Calinski-Harabasz index performs poorly in evaluating irregularly shaped clusters. MMJ-based internal clustering evaluation index uses MMJ distance and Semantic Center of Mass (SCOM) to revise the indices, so that it can evaluate irregularly shaped data. An experiment shows introducing MMJ distance to internal clustering evaluation index, can systematically improve the performance. We also devise two algorithms for calculating MMJ distance.

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Submission Number: 11972