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Convex Relaxation Methods for Community Detection
[article]
2018
arXiv
pre-print
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This paper surveys recent theoretical advances in convex optimization approaches for community detection. ...
We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. ...
implementations of these approaches for practical and large-scale problems. ...
arXiv:1810.00315v1
fatcat:6fk7op7iqvcq3h3aspsngv5e3y
Post-Processing Partitions to Identify Domains of Modularity Optimization
2017
Algorithms
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Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition ---i.e., the parameter-space domain where it has the largest modularity relative to the input set--- ...
We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational ...
The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies. ...
doi:10.3390/a10030093
pmid:29046743
pmcid:PMC5642987
fatcat:u7fen6fjezd63k5bu6cuc4oox4
Anomalous subgraph detection via Sparse Principal Component Analysis
2011
2011 IEEE Statistical Signal Processing Workshop (SSP)
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We characterize the anomaly in a subgraph via the well-known notion of network modularity, and we show that the optimization problem formulation resulting from our setup is very similar to a recently introduced ...
In this paper we investigate a problem with applicability to a wide variety of domains -detecting small, anomalous subgraphs in a background graph. ...
The reader is also referred to [11] for some previous related work on mathematical programming formulations for the related problem of modularity maximization. ...
doi:10.1109/ssp.2011.5967738
fatcat:lkmrxmp2zzewdpahgjk3jzrjzm
Detecting communities using asymptotical surprise
2015
Physical Review E
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2015 pre-print arXiv:1503.00445v1 fatcat:b3e7xyzjubgktkbj3ykpdkblqaOther Versions
Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. ...
This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. ...
Finally, We show the good performance of Surprise maximization for community detection, especially in large graphs with small communities. ...
doi:10.1103/physreve.92.022816
pmid:26382463
fatcat:rvedpcpm3nb67cllvy2ofuerw4
Identification of community structure in networks with convex optimization
[article]
2008
arXiv
pre-print
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We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization ...
We use our method to provide the first proof of optimality of a partition for a real-world network. ...
The author would like to thank the members of this project for this possibility. This paper presents research results of the project CARESSE of the pole MSTIC of Université Joseph Fourier, France. ...
arXiv:0806.1896v2
fatcat:vkl4jcdejjhvxmju4qgx5yr2w4
Modularity and Mutual Information in Networks: Two Sides of the Same Coin
[article]
2022
arXiv
pre-print
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Previous work on modularity has developed many efficient algorithms for modularity maximization. However, few of researchers considered the interpretation of the modularity function itself. ...
It can serve as both a standard benchmark to compare different community detection algorithms, and an optimization objective to detect communities itself. ...
Related Work Modularity was first proposed by [Newman and Girvan, 2004] as a stop criterion for another community detection algorithm. ...
arXiv:2103.02542v2
fatcat:ildimuoahbhqxhkjtz6wkk74gi
Additive Approximation Algorithms for Modularity Maximization
[article]
2016
arXiv
pre-print
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Community detection in graphs is now often conducted through modularity maximization: given an undirected graph G=(V,E), we are asked to find a partition C of V that maximizes the modularity. ...
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). ...
Quality functions in community detection return some value that represents the community-degree for a given partition of the set of vertices. ...
arXiv:1601.03316v1
fatcat:w2nqir2fqfdbbkiismxeuvi4hq
Additive Approximation Algorithms for Modularity Maximization
2016
International Symposium on Algorithms and Computation
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Community detection in graphs is now often conducted through modularity maximization: given an undirected graph G = (V, E), we are asked to find a partition C of V that maximizes the modularity. ...
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004) . ...
Quality functions in community detection return some value that represents the community-degree for a given partition of the set of vertices. ...
doi:10.4230/lipics.isaac.2016.43
dblp:conf/isaac/KawaseMM16
fatcat:dsq4yugxrzethbsuzc5rplyuwq
Applications of reformulations in mathematical programming
2012
4OR
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The third application considered in the thesis is that of computing the convex relaxation for multilinear problems, and to compare the "primal" formulation and another one obtained using a "dual" representation ...
The first problem tackled herein is graph clustering by means of modularity maximization. Since this problem is NP-hard, several heuristics are proposed. ...
However, modularity maximization remains a very interesting criterion for the detection of clusters; for the goal of this thesis, one of its most interesting properties is the fact that it can be described ...
doi:10.1007/s10288-012-0220-1
fatcat:47jmhf5adfg73joxngfmrsp44e
Quantitative function for community detection
2008
Physical Review E
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We propose a quantitative function for community partition-i.e., modularity density or D value. ...
communities. ...
So the community-detection problem can be viewed as a problem of finding a partition of a network such that its modularity density D is maximized. ...
doi:10.1103/physreve.77.036109
pmid:18517463
fatcat:rasvd7ixvzcatjsvlkgpbdbecq
Convexified Modularity Maximization for Degree-corrected Stochastic Block Models
[article]
2016
arXiv
pre-print
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Our approach is based on a convex programming relaxation of the classical (generalized) modularity maximization formulation, followed by a novel doubly-weighted ℓ_1 -norm k -median procedure. ...
This paper proposes a convexified modularity maximization approach for estimating the hidden communities under DCSBM. ...
Appendices A Supporting lemmas In this section we state several additional technical lemmas concerning random matrices. These lemmas are used in the proof of our main theorems. ...
arXiv:1512.08425v2
fatcat:kczixcdhejesznn5v2spzhypoe
Simplified Energy Landscape for Modularity Using Total Variation
2018
SIAM Journal on Applied Mathematics
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We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain---again, assuming the number of communities is known. ...
Furthermore, we show that modularity has no convex relaxation satisfying certain natural conditions. ...
Modularity also has a preferred scale for communities [25, 46] . ...
doi:10.1137/17m1138972
fatcat:odng4qt3vvcmxlf3z2bpjfzweq
Simplified Energy Landscape for Modularity Using Total Variation
[article]
2018
arXiv
pre-print
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We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain, again, assuming the number of communities is known. ...
They solve this problem, assuming the number of communities is known, using a Merriman, Bence, Osher (MBO) scheme. ...
modularity, and • any convergent subsequence of the u converges to a maximizer of modularity. ...
arXiv:1707.09285v3
fatcat:mv66timsonh4tlxtlj352yybwq
An ADMM Algorithm for Clustering Partially Observed Networks
[article]
2015
arXiv
pre-print
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In order to detect the underlying cluster structure, we propose a new convex formulation to decompose a partially observed adjacency matrix of a network into low-rank and sparse components. ...
Many of these algorithms are based on modularity maximization, and these methods suffer from the resolution limit. ...
for community detection. ...
arXiv:1410.3898v2
fatcat:vmdp6cnitrbajmkhrolhtxgjvy
Botnet Detection using Social Graph Analysis
[article]
2015
arXiv
pre-print
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The latter stage uses a refined modularity measure and formulates the problem as a non-convex optimization problem for which appropriate relaxation strategies are developed. ...
The method consists of two stages: (i) anomaly detection in an "interaction" graph among nodes using large deviations results on the degree distribution, and (ii) community detection in a social "correlation ...
Our criterion for "appropriate" is related to the well-known concept of modularity in community detection [17] , [18] , [19] . 2) Modularity-based Community Detection: The problem of community detection ...
arXiv:1503.02337v1
fatcat:2bujjptmanekhkjesndwiy6vza
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