Two Examples to Show How k-Means Reaches Richness and Consistency

Abstract

In [1] three axioms of clustering algorithms were introduced. In this paper, we demonstrated how k-Means clustering method reaches two of the three axioms: richness and consistency using two well-designed examples. For richness, a metric of form d(q ≥ 1) doesn't satisfy this property, but a semi-metric d(0 < q < 1) satisfies this property. For consistency, a counter-example is provided; however, this property is achieved in a more general sense when it comes to the Lloyd's algorithm [6], an approximation method for k-Means.