Abstract
Community detection in network-type data provides a powerful tool in analyzing and understanding real-world systems. In fact, community detection approaches aim to reduce the network’s dimensionality and partition it into a set of disjoint clusters or communities. However, real networks are usually corrupted with noise or outliers which affect the detected community structure quality. In this paper, a new robust community detection algorithm that is capable of recovering a clean or a smoothed version of the corrupted graph and detecting the correct community structure is introduced. The proposed approach combines robust principal component analysis (RPCA) and symmetric nonnegative matrix factorization (SymNMF) in a single optimization problem. The proposed problem is solved under the framework of alternating direction methods of multipliers (ADMM). In particular, the corrupted adjacency matrix is decomposed into a low-rank and sparse components using RPCA and the community structure is detected by applying SymNMF to the extracted low-rank component. Extensive experiments that have been conducted on real and simulated binary and weighted networks show that the proposed approach significantly outperforms existing algorithms in detecting the correct community structure even in grossly corrupted networks.
Highlights
In recent years, graph or network theory has become one of the most popular tools in modeling and analyzing relational data
An undirected weighted graph can be defined as G = {V, E, A} where V = {v1, . . . , vn} defines the set of nodes that models the objects in the network, and E defines the set of edges that models the pairwise similarities between the objects [6]. |V | and |E| are the number of nodes and edges in the network, respectively
The variables L, S, and M in the optimization problem are solved by alternating direction methods of multipliers (ADMM) and proximal algorithms assuming H is fixed until convergence
Summary
Graph or network theory has become one of the most popular tools in modeling and analyzing relational data. In SymNMF [10] [15], a symmetric nonnegative lower rank approximation is computed for the input nonnegative similarity matrix This low-rank approximation provides the nodes clustering assignment of the network.On the other hand, authors in [16] suggested dropping the symmetry for fast SymNMF. This will transfer the SymNMF problem to a nonsymmetric one and the idea from the state-ofthe-art algorithms for nonsymmetric NMF is adopted for the solution. The purpose of SAS-LP is to detect the communities that solve the problems related to instability, low quality and to possessing structural cohesiveness and attribute homogeneity Another local approach that depends on detecting and expansion of core nodes is proposed in [23].
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