Riemannian gradient-based Zhang neural network method for linear discriminant analysis

Yu-Hang Wang; Zhuo-Cheng Xie; Meng-Zhen Fu; Huan Ren; Yu-Hang Wang; Zhuo-Cheng Xie; Meng-Zhen Fu; Huan Ren

doi:10.3934/math.20261071

AIMS Mathematics

2026, Volume 11, Issue 8: 26699-26719. doi: 10.3934/math.20261071

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Research article

Riemannian gradient-based Zhang neural network method for linear discriminant analysis

School of Mathematical Sciences, Jiangxi Science and Technology Normal University, Nanchang, 330038, China

Received: 10 June 2026 Revised: 04 August 2026 Accepted: 19 August 2026 Published: 25 August 2026
MSC : 15A99, 65F99

Linear discriminant analysis (LDA) is a classic statistical method employed for classification and dimensionality reduction of large-scale datasets. In this paper, we propose a Zhang neural network method based on Riemannian gradient. Compared with traditional approaches for solving LDA, the proposed method achieves higher convergence accuracy, accelerated convergence speed, and reduced parameter sensitivity. In terms of theoretical analysis, we have investigated the properties and geometric dynamic characteristics, and provided stability analysis of the algorithm. Finally, through experiments with synthetic data and ORL face images, and by making a clear comparison with WH2, the advantages of the proposed algorithm were verified.
- linear discriminant analysis,
- Zhang neural network method,
- generalized Stiefel manifold,
- generalized Stiefel manifold
Citation: Yu-Hang Wang, Zhuo-Cheng Xie, Meng-Zhen Fu, Huan Ren. Riemannian gradient-based Zhang neural network method for linear discriminant analysis[J]. AIMS Mathematics, 2026, 11(8): 26699-26719. doi: 10.3934/math.20261071

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Abstract

Linear discriminant analysis (LDA) is a classic statistical method employed for classification and dimensionality reduction of large-scale datasets. In this paper, we propose a Zhang neural network method based on Riemannian gradient. Compared with traditional approaches for solving LDA, the proposed method achieves higher convergence accuracy, accelerated convergence speed, and reduced parameter sensitivity. In terms of theoretical analysis, we have investigated the properties and geometric dynamic characteristics, and provided stability analysis of the algorithm. Finally, through experiments with synthetic data and ORL face images, and by making a clear comparison with WH2, the advantages of the proposed algorithm were verified.

References

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