Spectral Clustering with Smooth Tiny Clusters

TL;DR

This paper introduces a novel spectral clustering algorithm that leverages data smoothness and tiny clusters to improve multi-scale clustering performance, outperforming existing methods.

Contribution

The paper proposes a new clustering method that incorporates data smoothness and tiny clusters, addressing limitations of traditional spectral clustering in multi-scale data.

Findings

Significantly outperforms state-of-the-art algorithms

Effectively handles multi-scale data with varying densities

Theoretically justified and experimentally validated

Abstract

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale data, as the distance varies a lot for clusters with different densities. State of the art(ROSC and CAST ) addresses this limitation by taking the reachability similarity of objects into account. However, we observe that in real-world scenarios, data in the same cluster tend to present in a smooth manner, and previous algorithms never take this into account. Based on this observation, we propose a novel clustering algorithm, which con-siders the smoothness of data for the first time. We first divide objects into a great many tiny clusters. Our key idea is to cluster tiny clusters, whose centers constitute smooth graphs. Theoretical analysis and experimental results show that our clustering algorithm significantly outperforms state of the art. Although in this paper, we singly focus on multi-scale situations, the idea of data smoothness can certainly be extended to any clustering algorithms