Community detection in dynamic graphs with missing edges

Abstract

Social networks are usually analyzed and mined without taking into account the presence of missing values. In this article, we consider dynamic networks represented by sequences of graphs that change over time and we study the robustness and the accuracy of the community detection algorithms in presence of missing edges. We assume that the network evolution can provide a complementary information allowing to neutralize the missing data. To confirm our hypothesis, we designed an experimental framework to simulate the missing data and compare the communities identified by the methods, with or without missing links. We explore two types of methods. The first ones, based on tensor decomposition, are adapted for dynamic networks. The second ones correspond to conventional community detection algorithms able to handle simple graphs. In our framework, the latter ones are adapted to dynamic graphs, either by merging the data during the preprocessing step or by merging the partitions during a post-processing step. The experimentation was conducted on synthetic and real dynamic networks for which the ground truth is available. The results confirm the best performances of the methods suited for dynamic networks when they present a complex community structure.

Maximum likelihood estimation of sparse networks with missing observations

“…On the other hand, the emergence of detailed data sets coming, for example, from social networks or genome sequencing has fostered new challenges, as their large size makes using the full data computationally unattractive. This has lead scientists to consider only sub-samples of the available data [7]. However, incomplete observation of the network structure may considerably affect the accuracy of inference methods [33].…”

Maximum Likelihood Estimation of Sparse Networks with Missing Observations

“…Note that for sparse graphs, ρn corresponds to the sparsity inducing sequence in equation ( 4). We need condition (7) to have the equivalence between the Frobenius distance and the Kullback-Leibler divergence. This assumption is systematic in the literature studying the maximum likelihood estimator for the stochastic block model as it guarantees that the loss associated to the maximum likelihood estimator is Lipschitz.…”

“…On the other hand, the emergence of detailed data sets coming, for example, from social networks or genome sequencing has fostered new challenges, as their large size makes using the full data computationally unattractive. This has lead scientists to consider only sub-samples of the available data [7]. However, incomplete observation of the network structure may considerably affect the accuracy of inference methods [32].…”

A new method for graph stream summarization based on both the structure and concepts

“…Community detection algorithms has many applications and recently, many articles [22][23][24][25][26] have been published on this subject. Graph summarization can be beneficial for detecting communities in a network.…”