基于改进的等距离映射算法的人脸识别

针对等距离映射(Isomap)算法在处理扰动图像时拓扑结构不稳定的缺点，提出了一种改进算法。改进算法将图像欧氏距离(IMED)嵌入到等距离映射算法之中。首先引入坐标度量系数计算图像的坐标度量矩阵，通过线性变换将原始图像从欧氏距离(ED)空间转换到图像欧氏距离空间；然后计算变换空间中样本的欧氏距离矩阵，并在此基础上构建样本邻域图，得到近似测地距离矩阵；最后采用多维标度(MDS)分析算法构造样本的低维表示。对ORL和Yale人脸数据库降维并结合最近邻分类器进行实验，基于改进算法的识别率平均分别提高了5.57%和3.95%，表明与原算法相比，改进算法在人脸识别中对图像扰动具有较好的鲁棒性。

Face recognition based on improved isometric feature mapping algorithm

Isometric feature mapping (Isomap) algorithm is topologically unstable if the input data are distorted. Therefore, an improved Isomap algorithm was proposed. In the improved algorithm, Image Euclidean Distance (IMED) was embedded into Isomap algorithm. Firstly, the authors transformed images into image Euclidean Distance (ED) space through a linear transformation by introducing metric coefficients and metric matrix; then, Euclidean distance matrix of images in the transformed space was calculated to find the neighborhood graph and geodesic distance matrix; finally, low-dimensional embedding was constructed by MultiDimensional Scaling (MDS) algorithm. Experiments with the improved algorithm and nearest-neighbor classifier were conducted on ORL and Yale face database. The results show that the proposed algorithm outperforms Isomap with average recognition rate by 5.57% and 3.95% respectively, and the proposed algorithm has stronger robustness for face recognition with small changes.