Community detection, which identifies densely connected node clusters with sparse between-group links, is vital for analyzing network structure and function in real-world systems. Most existing community detection methods based on GCNs primarily focus on node-level information while overlooking community-level features, leading to performance limitations on large-scale networks. To address this issue, we propose LQ-GCN, an overlapping community detection model from a local community perspective. LQ-GCN employs a Bernoulli-Poisson model to construct a community affiliation matrix and form an end-to-end detection framework. By adopting local modularity as the objective function, the model incorporates local community information to enhance the quality and accuracy of clustering results. Additionally, the conventional GCNs architecture is optimized to improve the model capability in identifying overlapping communities in large-scale networks. Experimental results demonstrate that LQ-GCN achieves up to a 33% improvement in Normalized Mutual Information (NMI) and a 26.3% improvement in Recall compared to baseline models across multiple real-world benchmark datasets.
Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network.
Accessing and gaining insight into the Rigveda poses a non-trivial challenge due to its extremely ancient Sanskrit language, poetic structure, and large volume of text. By using NLP techniques, this study identified topics and semantic connections of hymns within the Rigveda that were corroborated by seven well-known groupings of hymns. The 1,028 suktas (hymns) from the modern English translation of the Rigveda by Jamison and Brereton were preprocessed and sukta-level embeddings were obtained using, i) a novel adaptation of LSA, presented herein, ii) SBERT, and iii) Doc2Vec embeddings. Following an UMAP dimension reduction of the vectors, the network of suktas was formed using k-nearest neighbours. Then, community detection of topics in the sukta networks was performed with the Louvain, Leiden, and label propagation methods, whose statistical significance of the formed topics were determined using an appropriate null distribution. Only the novel adaptation of LSA using the Leiden method, had detected sukta topic networks that were significant (z = 2.726, p < .01) with a modularity score of 0.944. Of the seven famous sukta groupings analyzed (e.g., creation, funeral, water, etc.) the LSA derived network was successful in all seven cases, while Doc2Vec was not significant and failed to detect the relevant suktas. SBERT detected four of the famous suktas as separate groups, but mistakenly combined three of them into a single mixed group. Also, the SBERT network was not statistically significant.
The behavior of multivariate dynamical processes is often governed by underlying structural connections that relate the components of the system. For example, brain activity which is often measured via time series is determined by an underlying structural graph, where nodes represent neurons or brain regions and edges represent cortical connectivity. Existing methods for inferring structural connections from observed dynamics, such as correlation-based or spectral techniques, may fail to fully capture complex relationships in high-dimensional time series in an interpretable way. Here, we propose the use of path signatures a mathematical framework that encodes geometric and temporal properties of continuous paths to address this problem. Path signatures provide a reparametrization-invariant characterization of dynamical data and, in particular, can be used to compute the lead matrix which reveals lead-lag phenomena. We showcase our approach on time series from coupled oscillators in the Kuramoto model defined on a stochastic block model graph, termed the Kuramoto stochastic block model (KSBM). Using mean-field theory and Gaussian approximations, we analytically derive reduced models of KSBM dynamics in different temporal regimes and theoretically characterize the lead matrix in these settings. Leveraging these insights, we propose a novel signature-based community detection algorithm, achieving exact recovery of structural communities from observed time series in multiple KSBM instances. Our results demonstrate that path signatures provide a novel perspective on analyzing complex neural data and other high-dimensional systems, explicitly exploiting temporal functional relationships to infer underlying structure.
FastMap was first introduced in the Data Mining community for generating Euclidean embeddings of complex objects. In this dissertation, we first present FastMap to generate Euclidean embeddings of graphs in near-linear time: The pairwise Euclidean distances approximate a desired graph-based distance function on the vertices. We then apply the graph version of FastMap to efficiently solve various graph-theoretic problems of significant interest in AI: including facility location, top-K centrality computations, community detection and block modeling, and graph convex hull computations. We also present a novel learning framework, called FastMapSVM, by combining FastMap and Support Vector Machines. We then apply FastMapSVM to predict the satisfiability of Constraint Satisfaction Problems and to classify seismograms in Earthquake Science.
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.
Community detection in network analysis has become more intricate due to the recent hike in social networks (Cai et al., 2024). This paper suggests a new approach named ELPMeans that strives to address this challenge. For community detection in the whole network, ELPMeans combines Laplacian, Hierarchical Clustering as well as K-means algorithms. Our technique employs Laplacian centrality and minimum distance metrics for central node identification while k-means learning is used for efficient convergence to final community structure. Remarkably, ELPMeans is an unsupervised method which is not only simple to implement but also effectively tackles common problems such as random initialization of central nodes, or finding of number of communities (K). Experimental results show that our algorithm improves accuracy and reduces time complexity considerably outperforming recent approaches on real world networks. Moreover, our approach has a wide applicability range in various community detection tasks even with nonconvex shapes and no prior knowledge about the number of communities present.
The degree-corrected block model (DCBM), latent space model (LSM), and $\beta$-model are all popular network models. We combine their modeling ideas and propose the logit-DCBM as a new model. Similar as the $\beta$-model and LSM, the logit-DCBM contains nonlinear factors, where fitting the parameters is a challenging open problem. We resolve this problem by introducing a cancellation trick. We also propose R-SCORE as a recursive community detection algorithm, where in each iteration, we first use the idea above to update our parameter estimation, and then use the results to remove the nonlinear factors in the logit-DCBM so the renormalized model approximately satisfies a low-rank model, just like the DCBM. Our numerical study suggests that R-SCORE significantly improves over existing spectral approaches in many cases. Also, theoretically, we show that the Hamming error rate of R-SCORE is faster than that of SCORE in a specific sparse region, and is at least as fast outside this region.
Species interaction networks are a powerful tool for describing ecological communities; they typically contain nodes representing species, and edges representing interactions between those species. For the purposes of drawing abstract inferences about groups of similar networks, ecologists often use graph topology metrics to summarize structural features. However, gathering the data that underlies these networks is challenging, which can lead to some interactions being missed. Thus, it is important to understand how much different structural metrics are affected by missing data. To address this question, we analyzed a database of 148 real-world bipartite networks representing four different types of species interactions (pollination, host-parasite, plant-ant, and seed-dispersal). For each network, we measured six different topological properties: number of connected components, variance in node betweenness, variance in node PageRank, largest Eigenvalue, the number of non-zero Eigenvalues, and community detection as determined by four different algorithms. We then tested how these properties change as additional edges -- representing data that may have been missed -- are added to the networks. We found substantial variation in how robust different properties were to the missing data. For example, the Clauset-Newman-Moore and Louvain community detection algorithms showed much more gradual change as edges were added than the label propagation and Girvan-Newman algorithms did, suggesting that the former are more robust. Robustness also varied for some metrics based on interaction type. These results provide a foundation for selecting network properties to use when analyzing messy ecological network data.
Community detection is a cornerstone problem in social network analysis (SNA), aimed at identifying cohesive communities with minimal external links. However, the rise of generative AI and Metaverse introduce complexities by creating hybrid human-AI social networks (denoted by HASNs), where traditional methods fall short, especially in human-centric settings. This paper introduces a novel community detection problem in HASNs (denoted by MetaCD), which seeks to enhance human connectivity within communities while reducing the presence of AI nodes. Effective processing of MetaCD poses challenges due to the delicate trade-off between excluding certain AI nodes and maintaining community structure. To address this, we propose CUSA, an innovative framework incorporating AI-aware clustering techniques that navigate this trade-off by selectively retaining AI nodes that contribute to community integrity. Furthermore, given the scarcity of real-world HASNs, we devise four strategies for synthesizing these networks under various hypothetical scenarios. Empirical evaluations on real social networks, reconfigured as HASNs, demonstrate the effectiveness and practicality of our approach compared to traditional non-deep learning and graph neural network (GNN)-based methods.
Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized frameworks are not available for solving graph problems. Graph structures are ubiquitous in many applications around us and many graph problems have been widely studied over years. In recent times, there has been a surge in deep neural network based approaches to solve graph problems, with growing availability of graph structured datasets across diverse domains. Nevertheless, existing methods are mostly tailored to solve a specific task and lack the capability to create a generalized model leading to solutions for different downstream tasks. In this work, we propose a novel, resource-efficient framework named \emph{U}nified \emph{G}raph \emph{N}etwork (UGN) by leveraging the feature extraction capability of graph convolutional neural networks (GCN) and 2-dimensional convolutional neural networks (Conv2D). UGN unifies various graph learning tasks, such as link prediction, node classification, community detection, graph-to-graph translation, knowledge graph completion, and more, within a cohesive framework, while exercising minimal task-specific extensions (e.g., formation of supernodes for coarsening massive networks to increase scalability, use of \textit{mean target connectivity matrix} (MTCM) representation for achieving scalability in graph translation task, etc.) to enhance the generalization capability of graph learning and analysis. We test the novel UGN framework for six uncorrelated graph problems, using twelve different datasets. Experimental results show that UGN outperforms the state-of-the-art baselines by a significant margin on ten datasets, while producing comparable results on the remaining dataset.
In network research, Community Detection has always been a topic of significant interest in network science, with numerous papers and algorithms proposing to uncover the underlying structures within networks. In this paper, we conduct a comparative analysis of several prominent community detection algorithms applied to the SNAP Social Circles Dataset, derived from the Facebook Social Media network. The algorithms implemented include Louvain, Girvan-Newman, Spectral Clustering, K-Means Clustering, etc. We evaluate the performance of these algorithms based on various metrics such as modularity, normalized cut-ratio, silhouette score, compactness, and separability. Our findings reveal insights into the effectiveness of each algorithm in detecting various meaningful communities within the social network, shedding light on their strength and limitations. This research contributes to the understanding of community detection methods and provides valuable guidance for their application in analyzing real-world social networks.
Interpretability in reinforcement learning is crucial for ensuring AI systems align with human values and fulfill the diverse related requirements including safety, robustness and fairness. Building on recent approaches to encouraging sparsity and locality in neural networks, we demonstrate how the penalisation of non-local weights leads to the emergence of functionally independent modules in the policy network of a reinforcement learning agent. To illustrate this, we demonstrate the emergence of two parallel modules for assessment of movement along the X and Y axes in a stochastic Minigrid environment. Through the novel application of community detection algorithms, we show how these modules can be automatically identified and their functional roles verified through direct intervention on the network weights prior to inference. This establishes a scalable framework for reinforcement learning interpretability through functional modularity, addressing challenges regarding the trade-off between completeness and cognitive tractability of reinforcement learning explanations.
In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.
Graph Retrieval Augmented Generation (GRAG) is a novel paradigm that takes the naive RAG system a step further by integrating graph information, such as knowledge graph (KGs), into large-scale language models (LLMs) to mitigate hallucination. However, existing GRAG still encounter limitations: 1) simple paradigms usually fail with the complex problems due to the narrow and shallow correlations capture from KGs 2) methods of strong coupling with KGs tend to be high computation cost and time consuming if the graph is dense. In this paper, we propose the Fast Think-on-Graph (FastToG), an innovative paradigm for enabling LLMs to think ``community by community" within KGs. To do this, FastToG employs community detection for deeper correlation capture and two stages community pruning - coarse and fine pruning for faster retrieval. Furthermore, we also develop two Community-to-Text methods to convert the graph structure of communities into textual form for better understanding by LLMs. Experimental results demonstrate the effectiveness of FastToG, showcasing higher accuracy, faster reasoning, and better explainability compared to the previous works.
The integration of network information and node attribute information has recently gained significant attention in the community detection literature. In this work, we consider community detection in the Contextual Labeled Stochastic Block Model (CLSBM), where the network follows an LSBM and node attributes follow a Gaussian Mixture Model (GMM). Our primary focus is the misclassification rate, which measures the expected number of nodes misclassified by community detection algorithms. We first establish a lower bound on the optimal misclassification rate that holds for any algorithm. When we specialize our setting to the LSBM (which preserves only network information) or the GMM (which preserves only node attribute information), our lower bound recovers prior results. Moreover, we present an efficient spectral-based algorithm tailored for the CLSBM and derive an upper bound on its misclassification rate. Although the algorithm does not attain the lower bound, it serves as a reliable starting point for designing more accurate community detection algorithms (as many algorithms use spectral method as an initial step, followed by refinement procedures to enhance accuracy).
Clustering large high-dimensional datasets with diverse variable is essential for extracting high-level latent information from these datasets. Here, we developed an unsupervised clustering algorithm, we call "Village-Net". Village-Net is specifically designed to effectively cluster high-dimension data without priori knowledge on the number of existing clusters. The algorithm operates in two phases: first, utilizing K-Means clustering, it divides the dataset into distinct subsets we refer to as "villages". Next, a weighted network is created, with each node representing a village, capturing their proximity relationships. To achieve optimal clustering, we process this network using a community detection algorithm called Walk-likelihood Community Finder (WLCF), a community detection algorithm developed by one of our team members. A salient feature of Village-Net Clustering is its ability to autonomously determine an optimal number of clusters for further analysis based on inherent characteristics of the data. We present extensive benchmarking on extant real-world datasets with known ground-truth labels to showcase its competitive performance, particularly in terms of the normalized mutual information (NMI) score, when compared to other state-of-the-art methods. The algorithm is computationally efficient, boasting a time complexity of O(N*k*d), where N signifies the number of instances, k represents the number of villages and d represents the dimension of the dataset, which makes it well suited for effectively handling large-scale datasets.
The existence of salient semantic clusters in the latent spaces of a neural network during training strongly correlates its final accuracy on classification tasks. This paper proposes a novel fine-tuning method that boosts performance by optimising the formation of these latent clusters, using the Louvain community detection algorithm and a specifically designed clustering loss function. We present preliminary results that demonstrate the viability of this process on classical neural network architectures during fine-tuning on the CIFAR-100 dataset.
Criminals are using every means available to launder the profits from their illegal activities into ostensibly legitimate assets. Meanwhile, most commercial anti-money laundering systems are still rule-based, which cannot adapt to the ever-changing tricks. Although some machine learning methods have been proposed, they are mainly focused on the perspective of abnormal behavior for single accounts. Considering money laundering activities are often involved in gang criminals, these methods are still not intelligent enough to crack down on criminal gangs all-sidedly. In this paper, a systematic solution is presented to find suspicious money laundering gangs. A temporal-directed Louvain algorithm has been proposed to detect communities according to relevant anti-money laundering patterns. All processes are implemented and optimized on Spark platform. This solution can greatly improve the efficiency of anti-money laundering work for financial regulation agencies.
We study community detection in multiple networks whose nodes and edges are jointly correlated. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship patterns and correlated attributes across different platforms. Extending the classical Stochastic Block Model (SBM) and its contextual counterpart (CSBM), we introduce the correlated CSBM, which incorporates structural and attribute correlations across graphs. To build intuition, we first analyze correlated Gaussian Mixture Models, wherein only correlated node attributes are available without edges, and identify the conditions under which an estimator minimizing the distance between attributes achieves exact matching of nodes across the two databases. For correlated CSBMs, we develop a two-step procedure that first applies $k$-core matching to most nodes using edge information, then refines the matching for the remaining unmatched nodes by leveraging their attributes with a distance-based estimator. We identify the conditions under which the algorithm recovers the exact node correspondence, enabling us to merge the correlated edges and average the correlated attributes for enhanced community detection. Crucially, by aligning and combining graphs, we identify regimes in which community detection is impossible in a single graph but becomes feasible when side information from correlated graphs is incorporated. Our results illustrate how the interplay between graph matching and community recovery can boost performance, broadening the scope of multi-graph, attribute-based community detection.