The Importance of Good Starting Solutions in the Minimum Sum of Squares Clustering Problem

TL;DR

This paper introduces three algorithms for generating starting solutions in the Minimum Sum of Squares Clustering problem, demonstrating their effectiveness on various instances and achieving new best solutions.

Contribution

The paper presents novel algorithms for initial solution generation in clustering, improving solution quality and solving more challenging instances effectively.

Findings

Achieved five new best solutions on difficult instances.

Matched best known solutions on most medium and large instances.

Demonstrated the effectiveness of the proposed algorithms across diverse datasets.

Abstract

The clustering problem has many applications in Machine Learning, Operations Research, and Statistics. We propose three algorithms to create starting solutions for improvement algorithms for this problem. We test the algorithms on 72 instances that were investigated in the literature. Forty eight of them are relatively easy to solve and we found the best known solution many times for all of them. Twenty four medium and large size instances are more challenging. We found five new best known solutions and matched the best known solution for 18 of the remaining 19 instances.