Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unseeded low-rank graph matching by transform-based unsupervised point
  registration   The problem of learning a correspondence relationship between nodes of two
networks has drawn much attention of the computer science community and
recently that of statisticians. The unseeded version of this problem, in which
we do not know any part of the true correspondence, is a long-standing
challenge. For low-rank networks, the problem can be translated into an
unsupervised point registration problem, in which two point sets generated from
the same distribution are matchable by an unknown orthonormal transformation.
Conventional methods generally lack consistency guarantee and are usually
computationally costly.
  In this paper, we propose a novel approach to this problem. Instead of
simultaneously estimating the unknown correspondence and orthonormal
transformation to match up the two point sets, we match their distributions via
minimizing our designed loss function capturing the discrepancy between their
Laplace transforms, thus avoiding the optimization over all possible
correspondences. This dramatically reduces the dimension of the optimization
problem from $\Omega(n^2)$ parameters to $O(d^2)$ parameters, where $d$ is the
fixed rank, and enables convenient theoretical analysis. In this paper, we
provide arguably the first consistency guarantee and explicit error rate for
general low-rank models. Our method provides control over the computational
complexity ranging from $\omega(n)$ (any growth rate faster than $n$) to
$O(n^2)$ while pertaining consistency. We demonstrate the effectiveness of our
method through several numerical examples.

26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph