Graph Regularized And Low-rank Multi-label Linear Discriminant Analysis

Multi-label classification studies the problem that each instance is associated with a several of labels simultaneously. Comparing with traditional single-label classification, multi-label classification is more general, and it has been applied in many fields,such as multi-topic text categorization, image and video annotations, etc. Therefore,multi-label classification attracts more and more attentions, and many algorithms have been proposed. Among these algorithms, Multi-label Linear Discriminant Analysis(MLDA) is an effective method to deal with multi-label classification. However, MLDA can not capture the local geometric structure of data. This paper focuses on multilabel classification, and improves the MLDA. The main work of this paper is as follows:(1)The original MLDA based on classical Lineal Discriminant Analysis(LDA)to redefine the scatter matrices, and considering the label correlations. MLDA is an available algorithm for solving multi-label problems. However, MLDA neglects the local geometric structure of data, which is crucial for dimensionality reduction. In order to solve this problem, we employ a graph regularized term and present a new method called Graph Regularized Multi-label Linear Discriminant Analysis(GR-MLDA), which incorporates local structure into the framework of MLDA. The experimental results on several benchmark multi-label data sets demonstrate that our algorithm is feasible and effective.(2)In original MLDA, the computational complexity is very high when the dimensionality of data is high. In this paper, before solving the eigenproblem of GR-MLDA,we remove the null space of the scatter matrices so that the computation is optimized.The experimental results show that our computing method reduce the cost of computation effciently for high-dimensional data.(3)Existing discriminant methods assume that the data sets are clean, and noise free, and project samples into the subspace directly. As a result, they can not handle the outliers that caused by occlusion, specular re?ections or noise. In this paper, we introduce the low-rank matrix and sparse matrix and present a novel method Lowrank and Sparse Multi-label Linear Discriminant Analysis(LRS-MLDA). In the new method, the original data are decomposed into a low-rank matrix and a sparse matrix,so the outliers are removed. The experimental results show that our algorithm improve the original MLDA.