Clustering with Geometric Modularity
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: clustering, modularity
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TL;DR: We give a way to automatically tune the radius in DB-scan; this creates a fully hyper-parameter-free high-quality clustering algorithm.
Abstract: Clustering data is a fundamental problem in unsupervised learning with a range of applications in the natural and social sciences. This wide applicability has led to the development of dozens of clustering algorithms. Broadly, these algorithms can be divided as being (i) parametric, e.g. $k$-means, where the centers are parameters and $k$ a hyperparameter, and (ii) non-parametric, e.g. DB-Scan (Ester et al. 1996), which has hyperparameters, but otherwise only uses a density to find clustering. An attractive feature of DB-Scan is not needing to know the number of clusters (usually unknown in practice) in advance. In this work, we propose a new measure of cluster quality, called \emph{geometric modularity} and show how it can be used to obtain an improved algorithm based on DB-Scan. Through experiments on a wide-range of datasets we show that using geometric modularity yields a superior method. Interestingly, our experiments also show that this quantity tracks a \emph{supervised} measure called \emph{normalized mutual information} well, despite using no label information. Finally, we also provide a theoretical justification of the use of this measure by considering a model for well-clusterable data.
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Submission Number: 5676
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