Abstract:

As a simple and effective tool, linear regression has been widely used in pattern recognition. However, the direct projection from high-dimensional data to binary labels may not be flexible enough and suitable data rep-resentation for classification problems cannot be got. In order to solve this problem, the label relaxation method has been proposed. Although its effectiveness has been proven, the problems that it will increase the difference between targets from same class still exist. Therefore, an intra-class low-rank subspace learning (ICLRSL) method is pro-posed in this paper, which is different from the original linear regression and the label relaxation based method. Double projection matrices are used to perform intra-class low-rank subspace projection and label space projection respectively. The intra-class low-rank subspace obtained by ICLRSL is used as a bridge between the high-dimensional data space and the label space, and the preliminary coding of the data can be obtained, which has similar intra-class correlation with the final regression targets through intra-class low-rank constraint. At the same time, the row sparsity constraint ensures that the subspace projection focuses on the few features most relevant to the intra-class low-rank property, and reduces the negative impact of redundant information to some extent. Through the con-nection of intermediate subspace, on the one hand, it has more flexibility than directly learning a single projection matrix, and on the other hand, it can also obtain discriminative data representation. Experimental results on four public face datasets demonstrate the effectiveness of the ICLRSL algorithm.

Key words: face recognition, supervised learning, subspace projection, intra-class low-rank subspace

摘要：

线性回归作为简单有效的工具，在模式识别中已得到广泛使用。但是直接从高维数据到二元标签可能无法得到灵活的投影和适合分类问题的数据表示。针对这一问题，标签松弛技术被提出，虽然已经证明其有效性，但仍然存在增大同类差异的问题。因此，提出类内低秩的子空间学习（ICLRSL），不同于原始线性回归和基于标签松弛的方法，在使用原始二元标签的同时采用两个投影矩阵分别完成类内低秩子空间投影和标签空间投影。ICLRSL将类内低秩子空间作为高维数据空间到标签空间之间的桥梁，得到对数据的初步编码，通过类内低秩约束使其与最终的回归目标拥有类似的类内相关性。同时，行稀疏约束保证子空间投影关注与类内低秩最相关的少数特征，在一定程度上降低冗余信息带来的负面影响。通过中间子空间的连接，一方面比直接学习单个投影矩阵具备更多灵活性，另一方面也能得到判别的数据表示。在四个公开人脸数据集上的实验验证了ICLRSL算法的有效性。

关键词: 人脸识别, 监督学习, 子空间投影, 类内低秩子空间