Abstract: Aiming at the problem of the complexity of high dimensional small sample data during the process of KGE (kernel extension of graph embedding), by a fast calculation model based on KGE, this paper proposes a new KGE/CCA algorithm (KGE/CCA-S_t) which can reduce the computational complexity of kernel matrix. Firstly, sample data are projected into corresponding rank space of total scatter matrix in which the dimension is far lower than that in original sample space. Then, kernel canonical correlation analysis is used for feature extraction, the calculation of kernel matrix is decreased in this process. Through the simulation experiments on Yale face database and JAFFE face database, the results show that the recognition rate of the KGE/CCA algorithms is significantly better than that of KFD, KLPP and KNPE algorithms. Compared with the traditional KGE/CCA algorithm, KGE/CCA-S_t can effectively reduce the computation time without affecting the recognition rate.

Key words: kernel extension of graph, canonical correlation analysis, dimension reducing processing, scatter matrix

摘要： 针对高维小样本数据在核化图嵌入过程中出现的复杂度问题，引入基于核化图嵌入（kernel extension of graph embedding）的快速求解模型，提出了一种新的KGE/CCA算法（KGE/CCA-S_t）。首先将样本数据投影到维数远低于原样本空间维数的总体散度矩阵对应的秩空间，然后采用核典型相关分析进行特征提取，整个过程减少了核矩阵的计算量。在Yale人脸库和JAFFE人脸库上进行仿真实验，结果表明这种KGE/CCA算法的识别率明显优于KFD、KLPP和KNPE算法的识别率；和传统的KGE/CCA算法相比，在不影响识别率的情况下，KGE/CCA-S_t算法有效减少了计算时间。

关键词: 核化图, 典型相关分析, 降维处理, 散度矩阵