The Parallel Seeding Algorithm for k-Means Problem with Penalties

As a classic NP-hard problem in machine learning and computational geometry, the k-means problem aims to partition a data point set into k clusters such that the sum of the squared distance from each point to its nearest center is minimized. The k-means problem with penalties, denoted by k-MPWP, generalizing the k-means problem, allows that some points can be paid some penalties instead of being clustered. In this paper, we study the seeding algorithm of k-MPWP and propose a parallel seeding algorithm for k-MPWP along with the corresponding theoretical analysis.