Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identification of Overlapping Communities via Constrained Egonet Tensor
  Decomposition   Detection of overlapping communities in real-world networks is a generally
challenging task. Upon recognizing that a network is in fact the union of its
egonets, a novel network representation using multi-way data structures is
advocated in this contribution. The introduced sparse tensor-based
representation exhibits richer structure compared to its matrix counterpart,
and thus enables a more robust approach to community detection. To leverage
this structure, a constrained tensor approximation framework is introduced
using PARAFAC decomposition. The arising constrained trilinear optimization is
handled via alternating minimization, where intermediate subproblems are solved
using the alternating direction method of multipliers (ADMM) to ensure
convergence. The factors obtained provide soft community memberships, which can
further be exploited for crisp, and possibly-overlapping community assignments.
The framework is further broadened to include time-varying graphs, where the
edgeset as well as the underlying communities evolve through time. Performance
of the proposed approach is assessed via tests on benchmark synthetic graphs as
well as real-world networks. As corroborated by numerical tests, the proposed
tensor-based representation captures multi-hop nodal connections, that is,
connectivity patterns within single-hop neighbors, whose exploitation yields a
more robust community identification in the presence of mixing as well as
overlapping communities.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
2
The categories of this paper are: math