K-CDFs: A Nonparametric Clustering Algorithm via Cumulative Distribution Function

• Published in: Journal of computational and graphical statistics Vol. 32; no. 1; pp. 304 - 318
• Main Authors: Liu, Jicai, Li, Jinhong, Zhang, Riquan
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.01.2023; Taylor & Francis Ltd
• Subjects: Algorithms; Clustering; Distribution functions; Empirical analysis; Greedy algorithms; K-means; Nonparametric ANOVA; Nonparametric partitioning clustering; Nonparametric statistics; Probabilistic models; Projection mean variance; Spectral relaxation
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2022.2091575

We propose a novel partitioning clustering procedure based on the cumulative distribution function (CDF), called K-CDFs. For univariate data, the K-CDFs represent the cluster centers by empirical CDFs and assign each observation to the closest center measured by the Cram r-von Mises distance. The procedure is nonparametric and does not require assumptions on cluster distributions imposed by mixture models. A projection technique is used to generalize the K-CDFs for univariate data to an arbitrary dimension. The proposed procedure has several appealing properties. It is robust to heavy-tailed data, is not sensitive to the data dimensions, does not require moment conditions on data and can effectively detect linearly nonseparable clusters. To implement the K-CDFs, we propose two kinds of algorithms: a greedy algorithm as the classical Lloyd's algorithm and a spectral relaxation algorithm. We illustrate the finite sample performance of the proposed algorithms through simulation experiments and empirical analyses of several real datasets. Supplementary files for this article are available online.