Money laundering poses a significant challenge as it is estimated to account for 2%-5% of the global GDP. This has compelled regulators to impose stringent controls on financial institutions. One prominent laundering method for evading these controls, called smurfing, involves breaking up large transactions into smaller amounts. Given the complexity of smurfing schemes, which involve multiple transactions distributed among diverse parties, network analytics has become an important anti-money laundering tool. However, recent advances have focused predominantly on black-box network embedding methods, which has hindered their adoption in businesses. In this paper, we introduce GARG-AML, a novel graph-based method that quantifies smurfing risk through a single interpretable metric derived from the structure of the second-order transaction network of each individual node in the network. Unlike traditional methods, GARG-AML strikes an effective balance among computational efficiency, detection power and transparency, which enables its integration into existing AML workflows. To enhance its capabilities, we combine the GARG-AML score calculation with different tree-based methods and also incorporate the scores of the node's neighbours. An experimental evaluation on large-scale synthetic and open-source networks demonstrate that the GARG-AML outperforms the current state-of-the-art smurfing detection methods. By leveraging only the adjacency matrix of the second-order neighbourhood and basic network features, this work highlights the potential of fundamental network properties towards advancing fraud detection.
Attribute network embedding faces significant challenges, primarily integrating heterogeneous information and managing outliers. In this paper, we introduce a novel Robust Integrating Method by High-order Proximity for Self-supervised Attribute Network Embedding (RSANE). Firstly, a novel heterogeneous topological and semantic information integration method is designed, which contains arbitrary high-order proximity and theoretically includes summation and multiplication forms. Secondly, the RSANE can adaptively reduce the influence of outliers during the embedding process. By incorporating higher-order proximity, RSANE increases the score of outliers and achieves better robustness. Finally, through a deep architecture with dual autoencoders, RSANE achieves joint embedding of network structure and node attributes. In addition, introducing end-to-end reconstruction of structure and attributes can fully extract potential information. Moreover, extensive experiments associated with statistical tests and sensitivity analysis demonstrate that RSANE outperforms state-of-the-art algorithms across various downstream tasks. The code is available at https://github.com/wuzelong/RSANE.
Motivation: Network-based analyses of omics data are widely used, and while many of these methods have been adapted to single-cell scenarios, they often remain memory- and space-intensive. As a result, they are better suited to batch data or smaller datasets. Furthermore, the application of network-based methods in multi-omics often relies on similarity-based networks, which lack structurally-discrete topologies. This limitation may reduce the effectiveness of graph-based methods that were initially designed for topologies with better defined structures. Results: We propose Subset-Contrastive multi-Omics Network Embedding (SCONE), a method that employs contrastive learning techniques on large datasets through a scalable subgraph contrastive approach. By exploiting the pairwise similarity basis of many network-based omics methods, we transformed this characteristic into a strength, developing an approach that aims to achieve scalable and effective analysis. Our method demonstrates synergistic omics integration for cell type clustering in single-cell data. Additionally, we evaluate its performance in a bulk multi-omics integration scenario, where SCONE performs comparable to the state-of-the-art despite utilising limited views of the original data. We anticipate that our findings will motivate further research into the use of subset contrastive methods for omics data.
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This problem, known as network alignment, holds significant importance. It enhances our understanding of complex system structures and behaviours, facilitates the validation and extension of theoretical physics research about studying complex systems, and fosters diverse practical applications across various fields. However, due to variations in the structure, characteristics, and properties of complex networks across different fields, the study of network alignment is often isolated within each domain, with even the terminologies and concepts lacking uniformity. This review comprehensively summarizes the latest advancements in network alignment research, focusing on analyzing network alignment characteristics and progress in various domains such as social network analysis, bioinformatics, computational linguistics and privacy protection. It provides a detailed analysis of various methods' implementation principles, processes, and performance differences, including structure consistency-based methods, network embedding-based methods, and graph neural network-based (GNN-based) methods. Additionally, the methods for network alignment under different conditions, such as in attributed networks, heterogeneous networks, directed networks, and dynamic networks, are presented. Furthermore, the challenges and the open issues for future studies are also discussed.
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.
Many real-world and artificial systems and processes can be represented as graphs. Some examples of such systems include social networks, financial transactions, supply chains, and molecular structures. In many of these cases, one needs to consider a collection of graphs, rather than a single network. This could be a collection of distinct but related graphs, such as different protein structures or graphs resulting from dynamic processes on the same network. Examples of the latter include the evolution of social networks, community-induced graphs, or ego-nets around various nodes. A significant challenge commonly encountered is the absence of ground-truth labels for graphs or nodes, necessitating the use of unsupervised techniques to analyze such systems. Moreover, even when ground-truth labels are available, many existing graph machine learning methods depend on complex deep learning models, complicating model explainability and interpretability. To address some of these challenges, we have introduced NEExT (Network Embedding Exploration Tool) for embedding collections of graphs via user-defined node features. The advantages of the framework are twofold: (i) the ability to easily define your own interpretable node-based features in view of the task at hand, and (ii) fast embedding of graphs provided by the Vectorizers library. In this paper, we demonstrate the usefulness of NEExT on collections of synthetic and real-world graphs. For supervised tasks, we demonstrate that performance in graph classification tasks could be achieved similarly to other state-of-the-art techniques while maintaining model interpretability. Furthermore, our framework can also be used to generate high-quality embeddings in an unsupervised way, where target variables are not available.
Autism Spectrum Disorder (ASD) is a complex neurological condition characterized by varied developmental impairments, especially in communication and social interaction. Accurate and early diagnosis of ASD is crucial for effective intervention, which is enhanced by richer representations of brain activity. The brain functional connectome, which refers to the statistical relationships between different brain regions measured through neuroimaging, provides crucial insights into brain function. Traditional static methods often fail to capture the dynamic nature of brain activity, in contrast, dynamic brain connectome analysis provides a more comprehensive view by capturing the temporal variations in the brain. We propose BrainTWT, a novel dynamic network embedding approach that captures temporal evolution of the brain connectivity over time and considers also the dynamics between different temporal network snapshots. BrainTWT employs temporal random walks to capture dynamics across different temporal network snapshots and leverages the Transformer's ability to model long term dependencies in sequential data to learn the discriminative embeddings from these temporal sequences using temporal structure prediction tasks. The experimental evaluation, utilizing the Autism Brain Imaging Data Exchange (ABIDE) dataset, demonstrates that BrainTWT outperforms baseline methods in ASD classification.
Stability for dynamic network embeddings ensures that nodes behaving the same at different times receive the same embedding, allowing comparison of nodes in the network across time. We present attributed unfolded adjacency spectral embedding (AUASE), a stable unsupervised representation learning framework for dynamic networks in which nodes are attributed with time-varying covariate information. To establish stability, we prove uniform convergence to an associated latent position model. We quantify the benefits of our dynamic embedding by comparing with state-of-the-art network representation learning methods on three real attributed networks. To the best of our knowledge, AUASE is the only attributed dynamic embedding that satisfies stability guarantees without the need for ground truth labels, which we demonstrate provides significant improvements for link prediction and node classification.
The node2vec random walk has proven to be a key tool in network embedding algorithms. These random walks are tuneable, and their transition probabilities depend on the previous visited node and on the triangles containing the current and the previously visited node. Even though these walks are widely used in practice, most mathematical properties of node2vec walks are largely unexplored, including their stationary distribution. We study the node2vec random walk on community-structured household model graphs. We prove an explicit description of the stationary distribution of node2vec walks in terms of the walk parameters. We then show that by tuning the walk parameters, the stationary distribution can interpolate between uniform, size-biased, or the simple random walk stationary distributions, demonstrating the wide range of possible walks. We further explore these effects on some specific graph settings.
There are many approaches in mobile data ecosystem that inspect network traffic generated by applications running on user's device to detect personal data exfiltration from the user's device. State-of-the-art methods rely on features extracted from HTTP requests and in this context, machine learning involves training classifiers on these features and making predictions using labelled packet traces. However, most of these methods include external feature selection before model training. Deep learning, on the other hand, typically does not require such techniques, as it can autonomously learn and identify patterns in the data without external feature extraction or selection algorithms. In this article, we propose a novel deep learning based end-to-end learning framework for prediction of exposure of personally identifiable information (PII) in mobile packets. The framework employs a pre-trained large language model (LLM) and an autoencoder to generate embedding of network packets and then uses a triplet-loss based fine-tuning method to train the model, increasing detection effectiveness using two real-world datasets. We compare our proposed detection framework with other state-of-the-art works in detecting PII leaks from user's device.
Time-series prediction is increasingly popular in a variety of applications, such as smart factories and smart transportation. Researchers have used various techniques to predict power consumption, but existing models lack discussion of collaborative learning and privacy issues among multiple clients. To address these issues, we propose Multi-Head Heterogeneous Federated Learning (MHHFL) systems that consist of multiple head networks, which independently act as carriers for federated learning. In the federated period, each head network is embedded into 2-dimensional vectors and shared with the centralized source pool. MHHFL then selects appropriate source networks and blends the head networks as knowledge transfer in federated learning. The experimental results show that the proposed MHHFL systems significantly outperform the benchmark and state-of-the-art systems and reduce the prediction error by 24.9% to 94.1%. The ablation studies demonstrate the effectiveness of the proposed mechanisms in the MHHFL (head network embedding and selection mechanisms), which significantly outperforms traditional federated average and random transfer.
It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM. We further integrate NMM with our non-Euclidean graph variational autoencoder (VAE) framework, NMM-GNN. NMM-GNN learns embeddings through a unified framework which uses non-Euclidean GNN encoders, non-Euclidean Gaussian priors, a non-Euclidean decoder, and a novel space unification loss component to unify distinct non-Euclidean geometric spaces. Experiments on public datasets show NMM-GNN significantly outperforms state-of-the-art baselines on social network generation and classification tasks, demonstrating its ability to better explain how the social network is formed.
Link prediction is a fundamental task in graph analysis. Despite the success of various graph-based machine learning models for link prediction, there lacks a general understanding of different models. In this paper, we propose a unified framework for link prediction that covers matrix factorization and representative network embedding and graph neural network methods. Our preliminary methodological and empirical analyses further reveal several key design factors based on our unified framework. We believe our results could deepen our understanding and inspire novel designs for link prediction methods.
Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.
Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often relies on discrete steps that optimize the architecture and then train the parameters. We introduce a novel neural network training framework that fundamentally transforms the process by learning architecture and parameters simultaneously with gradient descent. With the appropriate setting of the loss function, it can discover sparse and compact neural networks for given datasets. Central to our approach is a multi-scale encoder-decoder, in which the encoder embeds pairs of neural networks with similar functionalities close to each other (irrespective of their architectures and weights). To train a neural network with a given dataset, we randomly sample a neural network embedding in the embedding space and then perform gradient descent using our custom loss function, which incorporates a sparsity penalty to encourage compactness. The decoder generates a neural network corresponding to the embedding. Experiments demonstrate that our framework can discover sparse and compact neural networks maintaining a high performance.
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate downstream tasks. In the field of NLP, word embedding spaces capture semantic relationships \textit{linearly}, allowing for information retrieval using \textit{simple linear operations} on word embedding vectors. Here, we demonstrate that there are structural properties of network data that yields this linearity. We show that the more homophilic the network representation, the more linearly separable the corresponding network embedding space, yielding better downstream analysis results. Hence, we introduce novel graphlet-based methods enabling embedding of networks into more linearly separable spaces, allowing for their better mining. Our fundamental insights into the structure of network data that enable their \textit{\textbf{linear}} mining and exploitation enable the ML community to build upon, towards efficiently and explainably mining of the complex network data.
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and efficient embedding technique based on approximate variants of equitable partitions. The approximation consists in introducing a user-tunable tolerance parameter relaxing the otherwise strict condition for exact equitable partitions that can be hardly found in real-world networks. We exploit a relationship between equitable partitions and equivalence relations for Markov chains and ordinary differential equations to develop a partition refinement algorithm for computing an approximate equitable partition in polynomial time. We compare our method against state-of-the-art embedding techniques on benchmark networks. We report comparable -- when not superior -- performance for visualization, classification, and regression tasks at a cost between one and three orders of magnitude smaller using a prototype implementation, enabling the embedding of large-scale networks which could not be efficiently handled by most of the competing techniques.
A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks, and various technical networks. There are many network embedding models have been proposed and developed for signed networks for both homogeneous and heterogeneous types. SG embedding learns low-dimensional vector representations for nodes of a network, which helps to do many network analysis tasks such as link prediction, node classification, and community detection. In this survey, we perform a comprehensive study of SG embedding methods and applications. We introduce here the basic theories and methods of SGs and survey the current state of the art of signed graph embedding methods. In addition, we explore the applications of different types of SG embedding methods in real-world scenarios. As an application, we have explored the citation network to analyze authorship networks. We also provide source code and datasets to give future direction. Lastly, we explore the challenges of SG embedding and forecast various future research directions in this field.
Network embedding has numerous practical applications and has received extensive attention in graph learning, which aims at mapping vertices into a low-dimensional and continuous dense vector space by preserving the underlying structural properties of the graph. Many network embedding methods have been proposed, among which factorization of the Personalized PageRank (PPR for short) matrix has been empirically and theoretically well supported recently. However, several fundamental issues cannot be addressed. (1) Existing methods invoke a seminal Local Push subroutine to approximate \textit{a single} row or column of the PPR matrix. Thus, they have to execute $n$ ($n$ is the number of nodes) Local Push subroutines to obtain a provable PPR matrix, resulting in prohibitively high computational costs for large $n$. (2) The PPR matrix has limited power in capturing the structural similarity between vertices, leading to performance degradation. To overcome these dilemmas, we propose PSNE, an efficient spectral s\textbf{P}arsification method for \textbf{S}caling \textbf{N}etwork \textbf{E}mbedding, which can fast obtain the embedding vectors that retain strong structural similarities. Specifically, PSNE first designs a matrix polynomial sparser to accelerate the calculation of the PPR matrix, which has a theoretical guarantee in terms of the Frobenius norm. Subsequently, PSNE proposes a simple but effective multiple-perspective strategy to enhance further the representation power of the obtained approximate PPR matrix. Finally, PSNE applies a randomized singular value decomposition algorithm on the sparse and multiple-perspective PPR matrix to get the target embedding vectors. Experimental evaluation of real-world and synthetic datasets shows that our solutions are indeed more efficient, effective, and scalable compared with ten competitors.
Decentralized social media platforms like Bluesky Social (Bluesky) have made it possible to publicly disclose some user behaviors with millisecond-level precision. Embracing Bluesky's principles of open-source and open-data, we present the first collection of the temporal dynamics of user-driven social interactions. BlueTempNet integrates multiple types of networks into a single multi-network, including user-to-user interactions (following and blocking users) and user-to-community interactions (creating and joining communities). Communities are user-formed groups in custom Feeds, where users subscribe to posts aligned with their interests. Following Bluesky's public data policy, we collect existing Bluesky Feeds, including the users who liked and generated these Feeds, and provide tools to gather users' social interactions within a date range. This data-collection strategy captures past user behaviors and supports the future data collection of user behavior.