Cluster Overlap as Objective Function

K-means uses the sum-of-squared error as the objective function to minimize within-cluster distances. We show that, as a consequence, it also maximizes between-cluster variances. This means that the two measures do not provide complementary information and that using only one is enough. Based on this property, we propose a new objective function called cluster overlap, which is measured intuitively as the proportion of points shared between the clusters. We adopt the new function within k-means and present an algorithm called overlap k-means. It is an alternative way to design a k-means algorithm. A localized variant is also provided by limiting the overlap calculation to the neighboring points.