On Parameter Tuning for Spectral Clustering: Two Simple, Fast, and Effective Criteria

Document Type

Article

Publication Date

1-1-2025

Publication Source

IEEE Access

Volume Number

13

First Page

181686

Last Page

181703

E-ISSN

21693536

Abstract

Spectral clustering is a modern clustering approach with many successful applications such as image segmentation and document grouping. However, it has faced two major challenges – high computational complexity and sensitivity of a scale parameter associated to the similarity function used. Since its introduction, much effort has been devoted to improving the scalability of spectral clustering, while little research has been conducted on parameter tuning. In this paper, we address the parameter tuning challenge of spectral clustering in a general context. We first recognize that the task of parameter tuning is equivalent to identifying a proper scale of the data set that corresponds to the natural clusters in it. We then propose two new criteria – relative k -means and relative NCut – for tuning the scale parameter used in similarity functions such as Gaussian and cosine. The relative k -means criterion examines the tightness of the clusters in the embedding space, whereas the relative NCut criterion is directly based on a spectral clustering objective. Experiments were conducted on a combination of synthetic and real data sets, which demonstrate the effectiveness of the proposed tuning techniques.

Keywords

Cosine similarity, Gaussian similarity, normalized cut, parameter tuning, scale learning, spectral clustering

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