This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph.

翻译：这是一份非线性维度和地物提取方法的教益和调查文件,以数据图的拉平面为基础。我们首先引入了相邻矩阵、拉平面矩阵的定义和对拉平面矩阵的解释。然后,我们覆盖了在数据子空间中应用集聚的图形和光谱集群的切割。解释了Lapalcian eigenmap的不同优化变体及其外标扩展。之后,我们引入了地方保存投影及其内核变体作为拉平面天体的线性特例。然后解释了图形嵌入的版本,这些版本是Laplacian eigenmap和地区保存投影的通用版本。最后,引入了扩散图,这是以数据图上的拉平面和随机散行法为基础的方法。