Sparse approximation to discriminant projection learning and application to image classification. (December 2019) - Yu, Yu-Feng; Ren, Chuan-Xian; Jiang, Min; Sun, Man-Yu; Dai, Dao-Qing; Guo, Guodong
Highlights: Developing a new estimation method of projection matrix to avoid the matrix singularity problem. Joint using of F-norm and L 2, 1 − norm to construct a feature selection framework, which is effective to select informative features. Proposing a supervised sparse discriminant projection learning algorithm, which preforms subspace learning and feature selection simultaneously. Proposing an effective optimization algorithm to solve the derived objective function, which can be theoretically proved for the convergence. Abstract: Subspace learning for dimensionality reduction is an important topic in pattern analysis and machine learning, and it has extensive applications in feature representation and image classification. Linear discriminant analysis (LDA) is a well-known subspace learning approach for supervised dimensionality reduction due to its effectiveness and efficacy in discriminant analysis. However, LDA is not stable and suffers from the singularity problem when addressing small sample size and high-dimensional data. In this paper, we develop a novel subspace learning model, named sparse approximation to discriminant projection learning (SADPL), to learn the sparse projection matrix. Different from the traditional LDA-based methods, we learn the projection matrix based on a new objective function rather than the Fisher criterion, which avoids the matrix singularity problem. In order to distinguish which features play an important role in discriminant analysis, we embed a feature selection framework to the subspace learning model to select the informative features. Finally, we can attain a convex objective function which can be solved by an effective optimization algorithm, and theoretically prove the convergence of the proposed optimization algorithm. Extensive experiments on all sorts of image classification tasks, such as face recognition, palmprint recognition, object categorization and texture classification show that our SADPL achieves competitive performance compared to the state-of-the-art methods.