Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Spectral Graph Embedding: A Non-Backtracking Perspective and Graph
  Approximation   Graph embedding has been proven to be efficient and effective in facilitating
graph analysis. In this paper, we present a novel spectral framework called
NOn-Backtracking Embedding (NOBE), which offers a new perspective that
organizes graph data at a deep level by tracking the flow traversing on the
edges with backtracking prohibited. Further, by analyzing the non-backtracking
process, a technique called graph approximation is devised, which provides a
channel to transform the spectral decomposition on an edge-to-edge matrix to
that on a node-to-node matrix. Theoretical guarantees are provided by bounding
the difference between the corresponding eigenvalues of the original graph and
its graph approximation. Extensive experiments conducted on various real-world
networks demonstrate the efficacy of our methods on both macroscopic and
microscopic levels, including clustering and structural hole spanner detection.

37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg