Elastic K-means using posterior probability

Abstract

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model.

Mixed-integer programming techniques for the minimum sum-of-squares clustering problem

“…For the assignment to be fixed, x pj has to be one. Due to Constraints (1b) or (2c), x pj can be seen as a kind of posterior probability of point p to belong to cluster j [61]. A good strategy for branching would be to select the point p for which the probabilities for each cluster assignment are almost the same.…”