Randomized Greedy Algorithms and Composable Coreset for k-Center Clustering with Outliers

TL;DR

This paper introduces a randomized greedy algorithm for k-center clustering with outliers that efficiently handles outliers, constructs small coresets in doubling metrics, and is suitable for distributed data, achieving near-optimal solutions with lower complexity.

Contribution

The paper presents a novel randomized greedy approach for k-center clustering with outliers, producing small coresets and enabling efficient distributed computation.

Findings

The randomized greedy algorithm effectively handles outliers in k-center clustering.

The method constructs small coresets in doubling metric spaces.

Experimental results show near-optimal solutions with reduced computational complexity.

Abstract

In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez's algorithm, that was developed for solving the ordinary $k$-center clustering problem. Based on some novel observations, we show that a simple randomized version of this greedy strategy actually can handle outliers efficiently. We further show that this randomized greedy approach also yields small coreset for the problem in doubling metrics (even if the doubling dimension is not given), which can greatly reduce the computational complexity. Moreover, together with the partial clustering framework proposed in arXiv:1703.01539 , we prove that our coreset method can be applied to distributed data with a low communication complexity. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower complexities comparing with the existing methods.