Torus Probabilistic Principal Component Analysis

Anahita Nodehi (), Mousa Golalizadeh (), Mehdi Maadooliat () and Claudio Agostinelli ()
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Anahita Nodehi: Tarbiat Modares University
Mousa Golalizadeh: Tarbiat Modares University
Mehdi Maadooliat: Marquette University
Claudio Agostinelli: University of Trento

Journal of Classification, 2025, vol. 42, issue 2, No 8, 435-456

Abstract: Abstract Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed spherical or toroidal in multivariate contexts. In this paper, we introduce a novel extension of probabilistic principal component analysis (PPCA) designed for toroidal (or torus) data, termed torus probabilistic PCA (TPPCA). We provide detailed algorithms for implementing TPPCA and demonstrate its applicability to torus data. To assess the efficacy of TPPCA, we perform comparative analyses using a simulation study and three real datasets. Our findings highlight the advantages and limitations of TPPCA in handling torus data. Furthermore, we propose statistical tests based on likelihood ratio statistics to determine the optimal number of components, enhancing the practical utility of TPPCA for real-world applications.

Keywords: Probabilistic principal component analysis; Non-euclidean space; Torus data; Wrapped normal distribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00357-025-09504-7

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