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Torus Probabilistic Principal Component Analysis

Author

Listed:
  • Anahita Nodehi

    (Tarbiat Modares University
    Institute for Research in Fundamental Sciences (IPM))

  • Mousa Golalizadeh

    (Tarbiat Modares University
    Institute for Research in Fundamental Sciences (IPM))

  • Mehdi Maadooliat

    (Marquette University)

  • Claudio Agostinelli

    (University of Trento)

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.

Suggested Citation

  • Anahita Nodehi & Mousa Golalizadeh & Mehdi Maadooliat & Claudio Agostinelli, 2025. "Torus Probabilistic Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 42(2), pages 435-456, July.
    • Handle: RePEc:spr:jclass:v:42:y:2025:i:2:d:10.1007_s00357-025-09504-7
    DOI: 10.1007/s00357-025-09504-7
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