Think globally, fit locally under the manifold setup: Asymptotic analysis of locally linear embedding
分析了局部线性嵌入（LLE）在流形设定下的渐近性质，指出一般流形下可能得不到拉普拉斯-贝尔特拉米算子，结果可能依赖非均匀采样，除非选择正确的正则化。推导了核函数，表明LLE不是马尔可夫过程，并与扩散图等算法比较。
Since its introduction in 2000, Locally Linear Embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of LLE under the manifold setup. We show that for a general manifold, asymptotically we may not obtain the Laplace–Beltrami operator, and the result may depend on nonuniform sampling unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that LLE is not a Markov process. A comparison with other commonly applied nonlinear algorithms, particularly a diffusion map, is provided and its relationship with locally linear regression is also discussed.