A1 Journal article (refereed)
Tandem clustering with invariant coordinate selection (2024)

Alfons, A., Archimbaud, A., Nordhausen, K., & Ruiz-Gazen, A. (2024). Tandem clustering with invariant coordinate selection. Econometrics and Statistics, In Press. https://doi.org/10.1016/j.ecosta.2024.03.002

JYU authors or editors

Publication details

All authors or editors: Alfons, Andreas; Archimbaud, Aurore; Nordhausen, Klaus; Ruiz-Gazen, Anne

Journal or series: Econometrics and Statistics

ISSN: 2452-3062

eISSN: 2452-3062

Publication year: 2024

Publication date: 16/03/2024

Volume: In Press

Publisher: Elsevier

Publication country: Netherlands

Publication language: English

DOI: https://doi.org/10.1016/j.ecosta.2024.03.002

Publication open access: Openly available

Publication channel open access: Partially open access channel

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2212.06108

Abstract

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

Keywords: multivariable methods; cluster analysis; principal component analysis

Free keywords: kmeans; principal component analysis; linear discriminant analysis; scatter matrices; minimum covariance determinant; robustness

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2024

Preliminary JUFO rating: 1