Clustering with Transitive Distance and K-Means Duality

TL;DR

This paper introduces a novel clustering method that uses transitive distance and K-means duality, achieving comparable accuracy to spectral clustering but with significantly reduced computational complexity and minimal parameter tuning.

Contribution

The proposed method offers a non-eigenproblem approach to clustering that handles complex data structures efficiently using transitive distance and K-means duality.

Findings

Achieves spectral clustering performance with $O(n^2)$ complexity

Handles complex, multi-scale, and noisy clusters effectively

Requires only the number of clusters as a parameter

Abstract

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a non-eigenproblem based clustering method is proposed to deal with the clustering problem. Its performance is comparable to the spectral clustering algorithms but it is more efficient with computational complexity $O(n^2)$. We show that with a transitive distance and an observed property, called K-means duality, our algorithm can be used to handle data sets with complex cluster shapes, multi-scale clusters, and noise. Moreover, no parameters except the number of clusters need to be set in our algorithm.