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

2026-03-11

AI Summary

This work addresses the high computational complexity and strong dimensionality dependence inherent in high-dimensional k-median clustering by proposing a learning-augmented approach that integrates noisy predicted labels. By designing an efficient sampling strategy and preprocessing mechanism, the method significantly reduces the algorithm’s exponential dependence on dimensionality while preserving useful prediction information. Both theoretical analysis and empirical evaluation demonstrate that the proposed approach substantially lowers computational overhead without compromising—and in some cases even improving—clustering quality, outperforming current state-of-the-art algorithms.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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 $α\in [0,1)$. 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.

Problem

• learning-augmented
• k-median clustering
• high dimensions
• computational complexity
• clustering cost

Innovation

• learning-augmented clustering
• k-median
• high-dimensional sampling
• dimensionality reduction
• computational complexity