Geometric partitioning-based multimodal linear discriminant analysis

Xinyi Han; Chaojie Wang; Xinyi Han; Chaojie Wang

doi:10.3934/math.20261048

AIMS Mathematics

2026, Volume 11, Issue 8: 26168-26185. doi: 10.3934/math.20261048

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Research article

Geometric partitioning-based multimodal linear discriminant analysis

Xinyi Han ,
Chaojie Wang ^,

School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China

Received: 06 June 2026 Revised: 30 July 2026 Accepted: 12 August 2026 Published: 24 August 2026
MSC : 15A18, 62H30, 68T10

Multimodal linear discriminant analysis(LDA), as an important method for cross-modal dimensionality reduction and feature fusion, has been extensively studied and applied in the field of pattern recognition. In this paper, a geometric partitioning-based multimodal linear discriminant analysis (GMLDA) method is proposed. The hyperplanes are constructed to partition the multimodal data within each class. The kernel principal component directions are used to determine the normal vectors of the hyperplanes, and they are served as the intra-class partitioning directions. The key point of the proposed method is the combination of hyperplanes, which makes the sample distribution within each modality more compact while increasing the separation between different modalities. Numerical results demonstrate the efficiency of the proposed GMLDA method by comparison with other multimodal LDA methods.
- linear discriminant analysis,
- multimodality,
- hyperplane,
- geometric partitioning,
- dimensionality reduction
Citation: Xinyi Han, Chaojie Wang. Geometric partitioning-based multimodal linear discriminant analysis[J]. AIMS Mathematics, 2026, 11(8): 26168-26185. doi: 10.3934/math.20261048

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Abstract

Multimodal linear discriminant analysis(LDA), as an important method for cross-modal dimensionality reduction and feature fusion, has been extensively studied and applied in the field of pattern recognition. In this paper, a geometric partitioning-based multimodal linear discriminant analysis (GMLDA) method is proposed. The hyperplanes are constructed to partition the multimodal data within each class. The kernel principal component directions are used to determine the normal vectors of the hyperplanes, and they are served as the intra-class partitioning directions. The key point of the proposed method is the combination of hyperplanes, which makes the sample distribution within each modality more compact while increasing the separation between different modalities. Numerical results demonstrate the efficiency of the proposed GMLDA method by comparison with other multimodal LDA methods.

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