J-Means: a new local search heuristic for minimum sum of squares clustering

Abstract

A new local search heuristic, called J-Means, is proposed for solving the minimum sum of squares clustering problem. The neighborhood of the current solution is defined by all possible centroid-to-entity relocations followed by corresponding changes of assignments. Moves are made in such neighborhoods until a local optimum is reached. The new heuristic is compared with two other well-known local search heuristics, K- and H-Means as well as with H-Means +, an improved version of the latter in which degeneracy is removed. Moreover, another heuristic, which fits into the variable neighborhood search metaheuristic framework and uses J-Means in its local search step, is proposed too. Results on standard test problems from the literature are reported. It appears that J-Means outperforms the other local search methods, quite substantially when many entities and clusters are considered.