Directed Clustering of Multivariate Data Based on Linear or Quadratic Latent Variable Models

Zhang, Yingjuan; Einbeck, Jochen

Abstract

We consider situations in which the clustering of some multivariate data is desired, which establishes an ordering of the clusters with respect to an underlying latent variable. As our motivating example for a situation where such a technique is desirable, we consider scatterplots of traffic flow and speed, where a pattern of consecutive clusters can be thought to be linked by a latent variable, which is interpretable as traffic density. We focus on latent structures of linear or quadratic shapes, and present an estimation methodology based on expectation–maximization, which estimates both the latent subspace and the clusters along it. The directed clustering approach is summarized in two algorithms and applied to the traffic example outlined. Connections to related methodology, including principal curves, are briefly drawn.

Citation

Zhang, Y., & Einbeck, J. (2024). Directed Clustering of Multivariate Data Based on Linear or Quadratic Latent Variable Models. Algorithms, 17(8), Article 358. https://doi.org/10.3390/a17080358

• Journal Article Type: Article
• Acceptance Date: Aug 13, 2024
• Online Publication Date: Aug 16, 2024
• Publication Date: 2024-08
• Deposit Date: Sep 13, 2024
• Publicly Available Date: Sep 13, 2024
• Journal: Algorithms
• Electronic ISSN: 1999-4893
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 8
• Article Number: 358
• DOI: https://doi.org/10.3390/a17080358
• Keywords: expectation–maximization algorithm, latent variable model, dimension reduction, fundamental diagram, clustering, mixture model, model selection
• Public URL: https://durham-repository.worktribe.com/output/2820421