Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and matrix factorization methods for consistent community
  detection in multi-layer networks   We consider the problem of estimating a consensus community structure by
combining information from multiple layers of a multi-layer network using
methods based on the spectral clustering or a low-rank matrix factorization. As
a general theme, these "intermediate fusion" methods involve obtaining a low
column rank matrix by optimizing an objective function and then using the
columns of the matrix for clustering. However, the theoretical properties of
these methods remain largely unexplored. In the absence of statistical
guarantees on the objective functions, it is difficult to determine if the
algorithms optimizing the objectives will return good community structures. We
investigate the consistency properties of the global optimizer of some of these
objective functions under the multi-layer stochastic blockmodel. For this
purpose, we derive several new asymptotic results showing consistency of the
intermediate fusion techniques along with the spectral clustering of mean
adjacency matrix under a high dimensional setup, where the number of nodes, the
number of layers and the number of communities of the multi-layer graph grow.
Our numerical study shows that the intermediate fusion techniques outperform
late fusion methods, namely spectral clustering on aggregate spectral kernel
and module allegiance matrix in sparse networks, while they outperform the
spectral clustering of mean adjacency matrix in multi-layer networks that
contain layers with both homophilic and heterophilic communities.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio