Approximation Algorithms for Spherical k-Means Problem with Penalties Using Local Search Techniques

Abstract

In this paper, we consider the spherical [Formula: see text]-means problem with penalties, a robust model of spherical clusterings that requires identifying outliers during clustering to improve the quality of the solution. Each outlier will incur a specified penalty cost. In this problem, one should detect the outliers and propose a [Formula: see text]-clustering for the given data set so as to minimize the sum of the clustering and penalty costs. As our main contribution, we present a [Formula: see text]-approximation via single-swap local search and an [Formula: see text]-approximation via multi-swap local search.