Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covariance, correlation matrix and the multi-scale community structure
  of networks   Empirical studies show that real world networks often exhibit multiple scales
of topological descriptions. However, it is still an open problem how to
identify the intrinsic multiple scales of networks. In this article, we
consider detecting the multi-scale community structure of network from the
perspective of dimension reduction. According to this perspective, a covariance
matrix of network is defined to uncover the multi-scale community structure
through the translation and rotation transformations. It is proved that the
covariance matrix is the unbiased version of the well-known modularity matrix.
We then point out that the translation and rotation transformations fail to
deal with the heterogeneous network, which is very common in nature and
society. To address this problem, a correlation matrix is proposed through
introducing the rescaling transformation into the covariance matrix. Extensive
tests on real world and artificial networks demonstrate that the correlation
matrix significantly outperforms the covariance matrix, identically the
modularity matrix, as regards identifying the multi-scale community structure
of network. This work provides a novel perspective to the identification of
community structure and thus various dimension reduction methods might be used
for the identification of community structure. Through introducing the
correlation matrix, we further conclude that the rescaling transformation is
crucial to identify the multi-scale community structure of network, as well as
the translation and rotation transformations.

6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci