On the Discrepancy between Kleinberg’s Clustering Axioms and k-Means Clustering Algorithm Behavior

Abstract This paper performs an investigation of Kleinberg’s axioms (from both intuitive and formal standpoint) as they relate to the well-known k -mean clustering method. The axioms, well a novel variations thereof, are analyzed in Euclidean space. A few natural properties proposed, resulting -means satisfying intuition behind (or, rather, small, variation on that intuition). In particular, two consistency property called centric motion consistency. It is shown these satisfied by k-means.