Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tangent Bundle Manifold Learning via Grassmann&Stiefel Eigenmaps   One of the ultimate goals of Manifold Learning (ML) is to reconstruct an
unknown nonlinear low-dimensional manifold embedded in a high-dimensional
observation space by a given set of data points from the manifold. We derive a
local lower bound for the maximum reconstruction error in a small neighborhood
of an arbitrary point. The lower bound is defined in terms of the distance
between tangent spaces to the original manifold and the estimated manifold at
the considered point and reconstructed point, respectively. We propose an
amplification of the ML, called Tangent Bundle ML, in which the proximity not
only between the original manifold and its estimator but also between their
tangent spaces is required. We present a new algorithm that solves this problem
and gives a new solution for the ML also.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics