Experiments with a non-convex variance-based clustering criterion

This paper investigates the effectiveness of a variance-based clustering criterion whose construct is similar to the popular minimum sum-of-squares or k-means criterion, except for two distinguishing characteristics: its ability to discriminate clusters by means of quadratic boundaries and its functional form, for which convexity does not hold. Using a recently proposed iterative local search heuristic that is suitable for general variance-based criteria—convex or not, the first to our knowledge that offers such broad support—the alternative criterion has performed remarkably well. In our experimental results, it is shown to be better suited for the majority of the heterogeneous real-world data sets selected. In conclusion, we offer strong reasons to believe that this criterion can be used by practitioners as an alternative to k-means clustering.