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arXiv · 1806.10403

Quantile-based clustering

Christian Hennig·Cinzia Viroli·Laura Anderlucci
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Abstract

A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and high-dimensional datasets. It allows for within-cluster skewness and internal variable scaling based on within-cluster variation. Different versions allow for different levels of parsimony and computational efficiency. Although $K$-quantiles clustering is conceived as nonparametric, it can be connected to a fixed partition model of generalized asymmetric Laplace-distributions. The consistency of $K$-quantiles clustering is proved, and it is shown that $K$-quantiles clusters correspond to well separated mixture components in a nonparametric mixture. In a simulation, $K$-quantiles clustering is compared with a number of popular clustering methods with good results. A high-dimensional microarray dataset is clustered by $K$-quantiles.

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Christian Hennig, Cinzia Viroli, Laura Anderlucci. 2018-06-27. Quantile-based clustering. https://arxiv.org/abs/1806.10403

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