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Publications of Nan Wu    :chronological  alphabetical  combined listing:

%% Papers Published   
   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 = {3805-3837},
   Publisher = {Institute of Mathematical Statistics},
   Year = {2018},
   Month = {January},
   url = {},
   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
   Doi = {10.1214/17-AOS1676},
   Key = {fds339455}
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