Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with
  Singularities   In this paper, we give a spectral approximation result for the Laplacian on
submanifolds of Euclidean spaces with singularities by the
$\epsilon$-neighborhood graph constructed from random points on the
submanifold. Our convergence rate for the eigenvalue of the Laplacian is
$O\left(\left(\log n/n\right)^{1/(m+2)}\right)$, where $m$ and $n$ denote the
dimension of the manifold and the sample size, respectively.

14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an