Abstract: Through introducing the column information of sample, this paper proposes an improved locality preserving projection (LPP) algorithm named adaptive neighbor and corresponding columns of the samples based graph construction method on LPP (ANCCG-LPP) to overcome the defects which parameter k is difficultly selected in traditional k-nearest neighbor graph and the original structure of the image sample is easily ignored by one dimensional vector of the sample for LPP. In the proposed algorithm, corresponding column neighbors of column samples are   determined adaptively by the column information of the samples, and then the neighbors of the sample are determined adaptively by the number of coupled column neighbors between two samples. Finally, the optimal projection vectors are solved by redefining the weight matrix to optimize the objective function. Supervised ANCCG-LPP algorithm based on ANCCG-LPP is put forward through adding class information of the samples. The simulation experiments on ORL, Yale Extended B face databases validate the effectiveness of the ANCCG-LPP and SANCCG-LPP.

Key words:  k-nearest neighbor, locality preserving projection, adaptive neighborhood, sample column, structural characteristics

摘要： 针对局部保持投影（locality preserving projection，LPP）算法在传统k近邻构图过程中出现的参数k选择困难问题和样本的一维向量容易忽略样本的原始结构特征问题，引入样本的列信息思想，提出了一种基于样本对应列信息的自适应邻域构图的局部保持投影算法（adaptive neighbor and corresponding columns based graph construction on LPP, ANCCG-LPP）。该算法根据样本间的列信息自适应地得出所有样本列的列近邻，然后根据样本间成对的列近邻个数自适应地确定样本的邻域；最后通过重新定义权值矩阵来优化目标函数进行最优投影向量集的求解。在ANCCG-LPP算法的基础上，通过加入样本的类别信息，提出了有监督的ANCCG-LPP算法。在ORL、Yale Extended B人脸库上的仿真实验验证了该算法的有效性。

关键词: k近邻, 局部保持投影, 自适应邻域, 样本列, 结构特征