Optimizing Lie Group SVM with Laplace Distribution for Robust Image Classification

As the foundation of artificial intelligence, mathematical theories, including statistics and group theory, are employed in this study to improve the Support Vector Machine (SVM), yielding favorable experimental results. For image data exhibiting heavy-tailed characteristics, this paper employs the Laplace distribution, which also possesses heavy-tailed properties, for modeling. As a sparse distribution, the Laplace distribution can address the analysis of continuous data with outliers. The distribution is then mapped to the Lie group manifold space to extract image features. It possess the geometric structure and differentiable properties of the Lie group, enabling the preservation of more transferred information during the mapping process. To optimize the measurement and computation of Lie group matrix features in SVM, several Lie group kernel functions and Riemannian space metrics are utilized to enhance SVM. Ultimately, the Lie group SVM method based on the Laplace distribution is obtained, which provides interpretability from the perspective of Lie group theory. The effectiveness and feasibility of the method are validated on two benchmark datasets, while its generalization capability is verified on two high-resolution remote sensing datasets, which demonstrates the superiority of the proposed method in image classification tasks.