基于Fisher判别准则的低秩矩阵恢复

摘要

The original dataset is decomposed into a set of representative bases with corresponding sparse errors for modeling the raw data in standard low-rank matrix recovery algorithm. Inspired by the Fisher criterion, a low-rank matrix recovery algorithm based on Fisher discriminate criterion is presented in this paper. Low-rank matrix recovery is executed in a supervised learning mode, i. e. , taking the within-class scatter and between-class scatter into account when the whole label information is available. The proposed model can be solved by the augmented Lagrange multipliers, and the additional discriminating ability is provided to the standard low-rank models for improving performance. The representative bases learned by the proposed algorithm are encouraged to be structurally coherent within the same class and be independent between classes as much as possible. Numerical simulations on face recognition tasks demonstrate that the proposed algorithm is competitive with the state-of-the-art alternatives.%标准的低秩矩阵恢复算法是把原始数据集分解成一组表征基和与此相应的稀疏误差，并以此分解对原始数据建模。受Fisher准则启发，文中提出基于带有Fisher判别准则的低秩矩阵恢复算法，在有监督学习模式下对低秩矩阵进行恢复，即当所有的标签信息都知道的情况下考虑类内散度和类间散度。文中所构造的模型可利用增广拉格朗日乘子法求解，并通过对标准的低秩矩阵模型增加判别性提高性能，利用文中算法所学习到的表征基使类内结构相关，而类间相互独立。在人脸识别问题上的仿真实验表明该算法的有效性。