Sample-and-Search: An Effective Algorithm for Learning-Augmented k-Median Clustering in High dimensions

TL;DR

This paper presents a new sampling-based algorithm for learning-augmented k-median clustering in high-dimensional spaces, reducing computational complexity and improving clustering quality through preprocessing with a predictor.

Contribution

The paper introduces a simple sampling method that enhances existing algorithms by lowering time complexity and dimensional dependency in learning-augmented k-median clustering.

Findings

Significant reduction in computational complexity.

Lower clustering cost achieved in experiments.

Effective handling of high-dimensional data.

Abstract

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$. This preprocessing step assigns potential labels to the points before clustering. We introduce an algorithm for this problem based on a simple yet effective sampling method, which substantially improves upon the time complexities of existing algorithms. Moreover, we mitigate their exponential dependency on the dimensionality of the Euclidean space. Lastly, we conduct experiments to compare our method with several state-of-the-art learning-augmented $k$-median clustering methods. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice, while achieving a lower clustering cost.