Robust Discriminant Feature Extraction Based On L2,1-norm And L1-norm

LDA(Linear Discriminant Analysis), also called FLDA(Fisher Linear Discriminant Analysis), is a typical subspace learning method, which aims to seek the projection matrix which can minimize the within-class scatter while simultaneously maximize the between-class scatter in the low-dimensional space. Due to its simplicity and good classification performance, LDA has been widely adopted to image recognition especially face recognition.However, LDA characterizes the similarity by L2-norm square, which leads to off-group points with large distance dominating the solution of the objective function. This lowers the performance of LDA in noised face recognition problem. In order to alleviate the problem, this article gives an in-depth-of study of robust discriminant feature extraction which includes L1-norm and L2,1-norm based LDA. A brief introduction is as below:1. Abstract the LDA trace ratio problem to be a common optimization problem, propose a framework to solve the problem with rigorous theoretical convergence analysis. This framework applies to not only LDA but also 2DLDA, 2DPCA, PCA et al.2. Due to the fact that existing L1-norm based robust discriminant feature extraction algorithms do not necessarily best optimize the corresponding objective which degrades performance, an iterative algorithm is proposed which simultaneously solves all the projection vectors by the above framework. This algorithm not only best optimizes the corresponding objective but also has better classification results. Experiments on AR, Yale B, PIE and COIL20 databases illustrate the effectiveness of our proposed algorithm.3. In order to alleviate the drawbacks of L1-norm similarity measurement, L2,1-norm based LDA is proposed by mathmatical analysis of LDA. Also, the above framework is adopted to develop another iterative algorithm which simultaneously solves all the projection vectors and whose convergence is rigorously proved. The propsed method is validated on three face databases(AR, Yale B and PIE) and gives better classification results over L1-norm based algorithms.