基于块对角投影表示的人脸识别

针对大多数特征表示算法在挖掘高维数据内在结构时容易受到噪声的影响，以及特征学习与分类器设计割裂导致分类性能降低的问题，提出了一种新的基于特征表示的人脸识别方法，称为块对角投影表示（BDPR）学习。首先，利用样本信息对每类样本的编码系数施加一个加权矩阵，通过局部约束来加强表示系数之间的相似性，从而降低噪声对系数学习的影响，使所提方法能够更好地保持数据的局部结构。其次，为了实现数据与编码系数相关联，降低表示系数的学习难度，构造了块对角化判别约束项来学习一个判别投影，通过投影从低维数据中提取样本表示系数，使系数包含更多的样本间全局结构信息且具有更低的计算复杂度。最后，将系数学习和分类器学习整合到同一框架下，同时增大不同类别样本间的“标签距离”，采用迭代求解的方式交替更新判别投影和分类器，最终得到最适合当前表示特征的分类器，使得所提方法能自动完成分类。多个公开的人脸数据集上的实验结果表明:较之传统的协作表示分类和多个主流的子空间学习方法，所提方法均取得了更优的识别效果。 

Block-diagonal projective representation for face recognition

Most feature representation algorithms are susceptible to noise when mining the internal structure of the high-dimensional data. Meanwhile, their feature learning and classifier design are separated, resulting in the limited classification performance in practice. Aimed at this issue, a new feature representation method, Block-Diagonal Projective Representation (BDPR), is proposed in this paper. First, a weighted matrix is imposed on the coding coefficients of samples over each class. By using such local constraints to enhance the similarity between the coefficients and reduce the impact of noise on coefficient learning, the proposed BDPR can well maintain the internal data structure. Second, to closely correlate the data with their coding coefficients and reduce the difficulty of learning the representation coefficients, we construct a block-diagonal constraint to learn a discriminative projection. In this way, the sample representation coefficients can be obtained in the low-dimensional projected subspace, which contains more global structure information between samples and enjoys lower computational complexity. Finally, the representation learning and classifier learning are integrated into the same framework. By increasing the "label distance" between samples of different classes, BDPR updates the discriminative projection and classifier in an iterative manner. In this way, the most suitable classifier can be found for the current optimal feature representation, making the proposed algorithm automatically realize the classification task. The results of experiments on multiple benchmark face datasets show that BDPR has achieved better recognition performance, compared to traditional collaborative representation based classification and several mainstream subspace learning algorithms.