Think globally, fit locally under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding [article]

Hau-Tieng Wu, Nan Wu
2017 arXiv   pre-print
Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of the LLE under the manifold setup. We show that for the general manifold, asymptotically we may not obtain the Laplace-Beltrami operator, and the result may depend on the non-uniform sampling, unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that the LLE is not a Markov process. A comparison
more » ... ith the other commonly applied nonlinear algorithms, particularly the diffusion map, is provided, and its relationship with the locally linear regression is also discussed.
arXiv:1703.04058v2 fatcat:gnpwp4krwvgv7n3i7vsne7j3xu