High-dimensional variable clustering based on maxima of a weakly dependent random process

• URL: http://arxiv.org/abs/2302.00934v3
• Date: Thu, 4 Jul 2024 10:13:29 GMT
• Title: High-dimensional variable clustering based on maxima of a weakly dependent random process
• Authors: Alexis Boulin, Elena Di Bernardino, Thomas Laloë, Gwladys Toulemonde,
• Abstract summary: We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm depending on a tuning parameter that recovers the clusters of variables without specifying the number of clusters empha priori.
• Score: 1.1999555634662633
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm depending on a tuning parameter that recovers the clusters of variables without specifying the number of clusters \emph{a priori}. Our work provides some theoretical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. A data-driven selection method for the tuning parameter is also proposed. To further illustrate the significance of our work, we applied our method to neuroscience and environmental real-datasets. These applications highlight the potential and versatility of the proposed approach.

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