基于QR分解的正则化邻域保持嵌入算法

Regularized neighborhood preserving embedding algorithm based on QR decomposition

针对训练样本不足时,对数据的低维子空间估计可能会产生严重偏差的问题,提出了一种基于QR分解的正则化邻域保持嵌入算法。首先,该算法定义一个局部拉普拉斯矩阵保留原始数据的局部结构;其次,将类内散度矩阵的特征谱空间划分成三个子空间,通过倒数谱模型定义的权值函数获得新的特征向量空间,进而对高维数据进行预处理;最后,定义一个邻域保持邻接矩阵,利用QR分解获得的投影矩阵和最近邻分类器进行人脸分类。与正则化广义局部保持投影(RGDLPP)算法相比,所提算法在ORL、Yale、FERET和PIE库上识别率分别提高了2个百分点、1.5个百分点、1.5个百分点和2个百分点。实验结果表明,所提算法易于实现,在小样本(SSS)下有较高的识别率。

The estimation of the low-dimensional subspace data may have serious deviation under lacking of the training samples. In order to solve the problem,a novel regularized neighborhood preserving embedding algorithm based on QR decomposition was proposed. Firstly,a local Laplace matrix was defined to preserve local structure of the original data.Secondly,the eigen spectrum space of within-class scatter matrix was divided into three subspaces,the new eigenvector space was obtained by inverse spectrum model defined weight function and then the preprocess of the high-dimensional data was achieved. Finally, a neighborhood preserving adjacency matrix was defined, the projection matrix obtained by QR decomposition and the nearest neighbor classifier were selected for face recognition. Compared with the Regularized Generalized Discriminant Locality Preserving Projection（ RGDLPP） algorithm,the recognition accuracy rate of the proposed method was respectively increased by 2 percentage points,1. 5 percentage points,1. 5 percentage points and 2 percentage points on ORL,Yale,FERET and PIE database. The experimental results show that the proposed algorithm is easy to implement and has high recognition rate relatively under Small Sample Size（ SSS）.