Clustering with Transitive Distance and K-Means Duality

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), 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). 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. Index Term – Clustering, duality, transitive distance, ultra-metric.

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