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@article{fds339455,
Author = {Wu, HT and Wu, N},
Title = {Think globally, fit locally under the manifold setup:
Asymptotic analysis of locally linear embedding},
Journal = {The Annals of Statistics},
Volume = {46},
Number = {6B},
Pages = {38053837},
Publisher = {Institute of Mathematical Statistics},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1214/17AOS1676},
Abstract = {© Institute of Mathematical Statistics, 2018. 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.},
Doi = {10.1214/17AOS1676},
Key = {fds339455}
}
