Discovering and tracking communities in time-varying networks is an important task in network science, motivated by applications in fields ranging from neuroscience to sociology. In this work, we characterize the celebrated family of spectral methods for static clustering in terms of the low-rank approximation of high-dimensional node embeddings. From this perspective, it becomes natural to view the evolving community detection problem as one of subspace tracking on the Grassmann manifold. While the resulting optimization problem is nonconvex, we adopt a block majorize-minimize Riemannian optimization scheme to learn the Grassmann geodesic which best fits the data. Our framework generalizes any static spectral community detection approach and leads to algorithms achieving favorable performance on synthetic and real temporal networks, including those that are weighted, signed, directed, mixed-membership, multiview, hierarchical, cocommunity-structured, bipartite, or some combination thereof. We demonstrate how to specifically cast a wide variety of methods into our framework, and demonstrate greatly improved dynamic community detection results in all cases.
Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency regularization on inter-community structures, inspired by the concept of minimal network topological changes within short intervals. Specifically, to address the representation collapse problem, we first introduce MFC, a matrix factorization-based deep graph clustering algorithm that preserves node embedding. Based on static clustering results, we construct probabilistic community networks and compute their persistence homology, a robust topological measure, to assess structural similarity between them. Moreover, a novel neural network regularization TopoReg is introduced to ensure the preservation of topological similarity between inter-community structures over time intervals. Our approach enhances temporal consistency and clustering accuracy on real-world datasets with both fixed and varying numbers of communities. It is also a pioneer application of TDA in temporally persistent community detection, offering an insightful contribution to field of network analysis. Code and data are available at the public git repository: https://github.com/kundtx/MFC_TopoReg
Large-scale online campaigns, malicious or otherwise, require a significant degree of coordination among participants, which sparked interest in the study of coordinated online behavior. State-of-the-art methods for detecting coordinated behavior perform static analyses, disregarding the temporal dynamics of coordination. Here, we carry out the first dynamic analysis of coordinated behavior. To reach our goal we build a multiplex temporal network and we perform dynamic community detection to identify groups of users that exhibited coordinated behaviors in time. Thanks to our novel approach we find that: (i) coordinated communities feature variable degrees of temporal instability; (ii) dynamic analyses are needed to account for such instability, and results of static analyses can be unreliable and scarcely representative of unstable communities; (iii) some users exhibit distinct archetypal behaviors that have important practical implications; (iv) content and network characteristics contribute to explaining why users leave and join coordinated communities. Our results demonstrate the advantages of dynamic analyses and open up new directions of research on the unfolding of online debates, on the strategies of coordinated communities, and on the patterns of online influence.
Network structure evolves with time in the real world, and the discovery of changing communities in dynamic networks is an important research topic that poses challenging tasks. Most existing methods assume that no significant change in the network occurs; namely, the difference between adjacent snapshots is slight. However, great change exists in the real world usually. The great change in the network will result in the community detection algorithms are difficulty obtaining valuable information from the previous snapshot, leading to negative transfer for the next time steps. This paper focuses on dynamic community detection with substantial changes by integrating higher-order knowledge from the previous snapshots to aid the subsequent snapshots. Moreover, to improve search efficiency, a higher-order knowledge transfer strategy is designed to determine first-order and higher-order knowledge by detecting the similarity of the adjacency matrix of snapshots. In this way, our proposal can better keep the advantages of previous community detection results and transfer them to the next task. We conduct the experiments on four real-world networks, including the networks with great or minor changes. Experimental results in the low-similarity datasets demonstrate that higher-order knowledge is more valuable than first-order knowledge when the network changes significantly and keeps the advantage even if handling the high-similarity datasets. Our proposal can also guide other dynamic optimization problems with great changes.
Dynamic community detection has been prospered as a powerful tool for quantifying changes in dynamic brain network connectivity patterns by identifying strongly connected sets of nodes. However, as the network science problems and network data to be processed become gradually more sophisticated, it awaits a better method to efficiently learn low dimensional representation from dynamic network data and reveal its latent function that changes over time in the brain network. In this work, an adversarial temporal graph representation learning (ATGRL) framework is proposed to detect dynamic communities from a small sample of brain network data. It adopts a novel temporal graph attention network as an encoder to capture more efficient spatio-temporal features by attention mechanism in both spatial and temporal dimensions. In addition, the framework employs adversarial training to guide the learning of temporal graph representation and optimize the measurable modularity loss to maximize the modularity of community. Experiments on the real-world brain networks datasets are demonstrated to show the effectiveness of this new method.
Dynamic community detection is the hotspot and basic problem of complex network and artificial intelligence research in recent years. It is necessary to maximize the accuracy of clustering as the network structure changes, but also to minimize the two consecutive clustering differences between the two results. There is a trade-off relationship between these two objectives. In this paper, we propose a Feature Transfer Based Multi-Objective Optimization Genetic Algorithm (TMOGA) based on transfer learning and traditional multi-objective evolutionary algorithm framework. The main idea is to extract stable features from past community structures, retain valuable feature information, and integrate this feature information into current optimization processes to improve the evolutionary algorithms. Additionally, a new theoretical framework is proposed in this paper to analyze community detection problem based on information theory. Then, we exploit this framework to prove the rationality of TMOGA. Finally, the experimental results show that our algorithm can achieve better clustering effects compared with the state-of-the-art dynamic network community detection algorithms in diverse test problems.
Cultural phylogenies, or "trees" of culture, are typically built using methods from biology that use similarities and differences in artifacts to infer the historical relationships between the populations that produced them. While these methods have yielded important insights, particularly in linguistics, researchers continue to debate the extent to which cultural phylogenies are tree-like or reticulated due to high levels of horizontal transmission. In this study, we propose a novel method for phylogenetic reconstruction using dynamic community detection that explicitly accounts for transmission between lineages. We used data from 1,498,483 collaborative relationships between electronic music artists to construct a cultural phylogeny based on observed population structure. The results suggest that, although the phylogeny is fundamentally tree-like, horizontal transmission is common and populations never become fully isolated from one another. In addition, we found evidence that electronic music diversity has increased between 1975 and 1999. The method used in this study is available as a new R package called DynCommPhylo. Future studies should apply this method to other cultural systems such as academic publishing and film, as well as biological systems where high resolution reproductive data is available, to assess how levels of reticulation in evolution vary across domains.
The study and comprehension of complex systems are crucial intellectual and scientific challenges of the 21st century. In this scenario, network science has emerged as a mathematical tool to support the study of such systems. Examples include environmental processes such as wildfires, which are known for their considerable impact on human life. However, there is a considerable lack of studies of wildfire from a network science perspective. Here, employing the chronological network concept -- a temporal network where nodes are linked if two consecutive events occur between them -- we investigate the information that dynamic community structures reveal about the wildfires' dynamics. Particularly, we explore a two-phase dynamic community detection approach, i.e., we applied the Louvain algorithm on a series of snapshots. Then we used the Jaccard similarity coefficient to match communities across adjacent snapshots. Experiments with the MODIS dataset of fire events in the Amazon basing were conducted. Our results show that the dynamic communities can reveal wildfire patterns observed throughout the year.
Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted evolving community structure, as a benchmark to compare and evaluate such algorithms. Unlike previously proposed benchmarks, it is able to specify any desired evolving community structure through a descriptive language, and then to generate the corresponding progressively evolving network. We empirically evaluate six existing algorithms for dynamic community detection in terms of instantaneous and longitudinal similarity with the planted ground truth, smoothness of dynamic partitions, and scalability. We notably observe different types of weaknesses depending on their approach to ensure smoothness, namely Glitches, Oversimplification and Identity loss. Although no method arises as a clear winner, we observe clear differences between methods, and we identified the fastest, those yielding the most smoothed or the most accurate solutions at each step.
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the evolution of mesoscale community structures. As a result, current methods do not provide useful tools to study and cannot explicitly capture temporal community dynamics. To address this challenge, we propose GRADE - a probabilistic model that learns to generate evolving node and community representations by imposing a random walk prior over their trajectories. Our model also learns node community membership which is updated between time steps via a transition matrix. At each time step link generation is performed by first assigning node membership from a distribution over the communities, and then sampling a neighbor from a distribution over the nodes for the assigned community. We parametrize the node and community distributions with neural networks and learn their parameters via variational inference. Experiments demonstrate GRADE outperforms baselines in dynamic link prediction, shows favourable performance on dynamic community detection, and identifies coherent and interpretable evolving communities.