Joint discriminant projection with cosine weighted dynamic graph regularization for feature extraction

Abstract

Obtaining low-dimensional discriminative features for original-dimensional data through projection in machine learning is challenging. The problems facing discriminative projection are: The data contains noise and outliers, and the effectiveness of the projection will be negatively affected. Extracting discriminative features by combining linear discriminative projection with preserving the local geometric structure is complex. The excess edges in the graph regularity term introduce redundant information, negatively impacting discriminative feature extraction. To address the issues above, the Joint Discriminant Projection with Cosine-Weighted Dynamic Graph Regularization (JDPCDG) is devised for feature extraction. The JDPCDG model consists of three main contributions: (1) The ${\xi }_1$-norm and ${\xi }_2$-norm are designed to adapt to outlier samples and noise features, respectively. (2) The $S_{cos}$ similarity graph matrix constructed with cosine weights is designed to preserve the global structure information within the class and obtain the local structure information in combination with the LDA model. (3) A framework model is constructed by effectively integrating manifold learning, linear discriminant analysis, and reconstructed data. Comprehensive experiments on synthetic data and multiple real-world datasets consistently demonstrate their superior performance over other relevant feature extraction methods. Experiments are conducted on non-image and image data, comparing them with related methods. The experimental results verify the robustness and superiority of the proposed JDPCDG.