Locally Joint Sparse Marginal Embedding for Feature Extraction

Dongmei Mo, Zhihui Lai, Wai-Keung Wong

Abstract: Classical linear discriminant analysis (LDA) has the limitation that it requires the within-class scatter matrix to be nonsingular so that it can perform eigen-decomposition to obtain optimal solutions. To break through this limitation, many methods based on LDA have been proposed. However, these methods are either sensitive to outliers or lack joint sparsity for effective feature extraction. To release these problems, this paper proposes a locally joint sparse marginal embedding (LJSME) method. LJSME reconstructs the scatter matrices and utilizes the locality graph to weigh each pair of data, such that it is robust to outliers and able to preserve the neighborhood relationship of the data. Moreover, LJSME can easily avoid the small sample-size problem by a maximum margin criterion and obtain joint sparsity for effective feature extraction by using joint sparse regularization. The comprehensive analysis between the proposed LJSME and the related methods is presented, which indicates the advantages of the proposed method. A series of experiments was conducted to evaluate the performance of LJSME when compared with the state-of-the-art methods. The MATLAB code of LJSME can be downloaded from https://github.com/TungmeeMo/LJSME.git .