Robust sparse manifold discriminant analysis

Classical linear discriminant analysis (LDA) has been applied to machine learning and pattern recognition successfully, and many variants based on LDA are proposed. However, the traditional LDA has several disadvantages as follows: Firstly, since the features selected by feature selection have good interpretability, LDA has poor performance in feature selection. Secondly, there are many redundant features or noisy data in the original data, but LDA has poor robustness to noisy data and outliers. Lastly, LDA only utilizes the global discriminant information, without consideration for the local discriminant structure. In order to overcome the above problems, we present a robust sparse manifold discriminant analysis (RSMDA) method. In RSMDA, by introducing the L-2,L-1 norm, the most discriminant features can be selected for discriminant analysis. Meanwhile, the local manifold structure is used to capture the local discriminant information of the original data. Due to the introduction of L-2,L-1 constraints and local discriminant information, the proposed method has excellent robustness to noisy data and has the potential to perform better than other methods. A large number of experiments on different data sets have proved the good effectiveness of RSMDA.