鲁棒拉普拉斯特征映射算法*

研究拉普拉斯特征映射算法（Laplacian eigenmap，LE）对离群点的敏感性，提出一种具有鲁棒性的拉普拉斯特征映射算法（robust Laplacian eigenmap，RLE）。该方法在离群点检测的基础上，利用鲁棒PCA算法（robust PCA，RPCA）对离群点进行局部光滑化处理，将离群点和其邻域投影到低维的局部切空间上，再构造能够准确反映离群点局部邻域关系的对应权值，减少离群点对Laplacian矩阵的影响。模拟实验和实际例子都证明，通过这种方法构造的鲁棒拉普拉斯特征映射算法，对于离群

Robust Laplacian eigenmap

This paper focused on the sensitivity of Laplacian eigenmap (LE) to outliers, and presented a robust Laplacian eigenmap (RLE). RLE was base on the outlier detection, projected the outliers and their neighbors to the low-dimensional tangent space with the robust PCA method. In the low-dimensional tangent space, RLE constructed the to weight graph connected the outliers and their neighbors, which could reflect the intrinsic local geometry of the outliers.The algorithm reduced the impact of outliers on the Laplacian matrix. Simulation and real examples show that RLE is robust against outliers.