Linear Discriminant Analysis with Gradient Optimization on Covariance Inverse

• URL: http://arxiv.org/abs/2506.06845v1
• Date: Sat, 07 Jun 2025 15:50:43 GMT
• Title: Linear Discriminant Analysis with Gradient Optimization on Covariance Inverse
• Authors: Cencheng Shen, Yuexiao Dong,
• Abstract summary: Linear discriminant analysis (LDA) is a fundamental method in statistical pattern recognition and classification.<n>In this work, we propose LDA with gradient optimization (LDA-GO), a new approach that directly optimize the inverse covariance matrix via gradient descent.<n>The algorithm parametrizes the inverse covariance matrix through Cholesky factorization, incorporates a low-rank extension to reduce computational complexity, and considers a multiple-initialization strategy.
• Score: 4.872570541276082
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Linear discriminant analysis (LDA) is a fundamental method in statistical pattern recognition and classification, achieving Bayes optimality under Gaussian assumptions. However, it is well-known that classical LDA may struggle in high-dimensional settings due to instability in covariance estimation. In this work, we propose LDA with gradient optimization (LDA-GO), a new approach that directly optimizes the inverse covariance matrix via gradient descent. The algorithm parametrizes the inverse covariance matrix through Cholesky factorization, incorporates a low-rank extension to reduce computational complexity, and considers a multiple-initialization strategy, including identity initialization and warm-starting from the classical LDA estimates. The effectiveness of LDA-GO is demonstrated through extensive multivariate simulations and real-data experiments.

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