In the big data era, spatial-network data has become increasingly important and popular in many real-world objects, ranging from micro-scale (e.g., molecule structures), to middle-scale (e.g., biological neural networks), to macro-scale (e.g., mobility networks). Spatial networks consist of nodes and edges that are embedded in a geometric space. Although, it is critical to model and understand the generative process of spatial networks, this task remains largely under-explored due to the significant difficulty in automatically modeling and distinguishing the dependency and relevance among various spatial and network semantic factors. In addition, containing both spatial and network information makes the modeling of spatial networks bear large time and memory cost, especially for large graphs. To address the aforementioned challenges, we first propose a novel objective for joint spatial-network disentangled representation learning from the perspective of information bottleneck as well as a novel progressive optimization algorithm to optimize the intractable objective. Based on this, a Spatial-Network Disentangled Variational Autoencoder (SND-VAE) is proposed to discover the independent and dependent latent factors of spatial and networks. To reduce the time complexity, an efficient version SND-VAE-light is proposed, which is based on a novel Efficient Spatial-Network Message Passing Neural Network (ES-MPNN). Qualitative and quantitative experiments on both synthetic and real-world datasets with various scales of graph size demonstrate the superiority of the proposed model over the state-of-the-arts by up to 66.9% for graph generation and 37.3% for interpretability. In addition, the ES-MPNN is also proved to reduce the time complexity of the encoder in the generative model from cubic to linear growth (The implementation of this work can be found at https://github.com/xguo7/SND-VAE ).

Deep learning has shown remarkable success in the field of clustering recently. However, how to transfer a trained clustering model on a source domain to a target domain by leveraging the acquired knowledge to guide the clustering process remains challenging. Existing deep clustering methods often lack generalizability to new domains because they typically learn a group of fixed cluster centroids, which may not be optimal for the new domain distributions. In this paper, we propose a novel transferable deep clustering model that can automatically adapt the cluster centroids according to the distribution of data samples. Rather than learning a fixed set of centroids, our approach introduces a novel attention-based module that can adapt the centroids by measuring their relationship with samples. In addition, we theoretically show that our model is strictly more powerful than some classical clustering algorithms such as k-means or Gaussian Mixture Model (GMM). Experimental results on both synthetic and real-world datasets demonstrate the effectiveness and efficiency of our proposed transfer learning framework, which significantly improves the performance on target domain and reduces the computational cost.

Text-Attributed Graphs (TAGs) enhance graph structures with natural language descriptions, enabling detailed representation of data and their relationships across a broad spectrum of real-world scenarios. Despite the potential for deeper insights, existing TAG representation learning primarily omit the semantic relationship among node texts, and mostly relies on supervised methods, necessitating extensive labeled data and limiting applicability across diverse contexts. This paper introduces a new self-supervised learning framework, Text-Attributed-Graph Multi-View Alignment (TAGA), which overcomes these constraints by integrating TAGs' structural and semantic dimensions. TAGA constructs two complementary views: Text-of-Graph view, which organizes node texts into structured documents based on graph topology, and the Graph-of-Text view, which converts textual nodes and connections into graph data. By aligning representations from both views, TAGA captures joint textual and structural information. In addition, a novel structure-preserving random walk algorithm is proposed for efficient training on large-sized TAGs. Our framework demonstrates strong performance in zero-shot and few-shot scenarios across eight real-world datasets.

Research question answering requires accurate retrieval and contextual understanding of scientific literature. However, current Retrieval-Augmented Generation (RAG) methods often struggle to balance complex document relationships with precise information retrieval. In this paper, we introduce Contextualized Graph Retrieval-Augmented Generation (CG-RAG), a novel framework that integrates sparse and dense retrieval signals within graph structures to enhance retrieval efficiency and subsequently improve generation quality for research question answering. First, we propose a contextual graph representation for citation graphs, effectively capturing both explicit and implicit connections within and across documents. Next, we introduce Lexical-Semantic Graph Retrieval (LeSeGR), which seamlessly integrates sparse and dense retrieval signals with graph encoding. It bridges the gap between lexical precision and semantic understanding in citation graph retrieval, demonstrating generalizability to existing graph retrieval and hybrid retrieval methods. Finally, we present a context-aware generation strategy that utilizes the retrieved graph-structured information to generate precise and contextually enriched responses using large language models (LLMs). Extensive experiments on research question answering benchmarks across multiple domains demonstrate that our CG-RAG framework significantly outperforms RAG methods combined with various state-of-the-art retrieval approaches, delivering superior retrieval accuracy and generation quality.

Text-Attributed Graphs (TAGs) are graphs of connected textual documents. Graph models can efficiently learn TAGs, but their training heavily relies on human-annotated labels, which are scarce or even unavailable in many applications. Large language models (LLMs) have recently demonstrated remarkable capabilities in few-shot and zero-shot TAG learning, but they suffer from scalability, cost, and privacy issues. Therefore, in this work, we focus on synergizing LLMs and graph models with their complementary strengths by distilling the power of LLMs into a local graph model on TAG learning. To address the inherent gaps between LLMs (generative models for texts) and graph models (discriminative models for graphs), we propose first to let LLMs teach an interpreter with rich rationale and then let a student model mimic the interpreter's reasoning without LLMs' rationale. We convert LLM's textual rationales to multi-level graph rationales to train the interpreter model and align the student model with the interpreter model based on the features of TAGs. Extensive experiments validate the efficacy of our proposed framework.

Semantic trajectories, which enrich spatial-temporal data with textual information such as trip purposes or location activities, are key for identifying outlier behaviors critical to healthcare, social security, and urban planning. Traditional outlier detection relies on heuristic rules, which requires domain knowledge and limits its ability to identify unseen outliers. Besides, there lacks a comprehensive approach that can jointly consider multi-modal data across spatial, temporal, and textual dimensions. Addressing the need for a domain-agnostic model, we propose the Transferable Outlier Detection for Human Semantic Trajectories (TOD4Traj) framework. TOD4Traj first introduces a modality feature unification module to align diverse data feature representations, enabling the integration of multi-modal information and enhancing transferability across different datasets. A contrastive learning module is further proposed for identifying regular mobility patterns both temporally and across populations, allowing for a joint detection of outliers based on individual consistency and group majority patterns. Our experimental results have shown TOD4Traj's superior performance over existing models, demonstrating its effectiveness and adaptability in detecting human trajectory outliers across various datasets.

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such as neuron morphology and river geomorphology, but traditional graph representation methods often overlook these specific characteristics of tree structures. To address this, we introduce a new representation learning framework tailored for geometric trees. It first features a unique message passing neural network, which is both provably geometrical structure-recoverable and rotation-translation invariant. To address the data label scarcity issue, our approach also includes two innovative training targets that reflect the hierarchical ordering and geometric structure of these geometric trees. This enables fully self-supervised learning without explicit labels. We validate our method's effectiveness on eight real-world datasets, demonstrating its capability to represent geometric trees.

Many real-world networks, such as graph-structured molecules or social networks, exhibit latent hierarchical structures at many different resolutions. Existing hierarchical graph neural networks (GNNs) mainly focus on modifying graph global pooling regions into partitioned clusters, while keeping the convolutional layers unchanged. However, these approaches may suffer from a loss of expressive power in learned representations due to the uncontrolled growth of the neighborhood, leading to a failure in capturing true hierarchies. Furthermore, many real-world hierarchical graphs possess an underlying fractal structure, which is crucial to unraveling the formation mechanism of networks. Unfortunately, existing hierarchical GNNs often overlook this important aspect of graph hierarchy. To tackle these challenges, this paper proposes a generic framework for hierarchical network representation learning. We propose the Self-Similar Graph Neural Network (SS-GNN), which leverages localized representations by excluding redundant nodes and edges. At each resolution of the coarsened map, SS-GNN extracts both intra- and inter-cluster embeddings to preserve the discriminative power of the model with a theoretical guarantee. To exploit the graph fractal structure, we introduce a novel module for measuring self-similarity between resolutions and a characterized objective function for automatic adjustment of model parameters. We demonstrate the strength of our proposed framework through extensive experiments on 13 real-world datasets by outperforming the state-of-the-art GNN models.

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore, merely combining individual spatial and network representations cannot reveal the underlying interaction mechanism of spatial networks. Besides, existing spatial network representation learning methods can only consider networks embedded in Euclidean space, and can not well exploit the rich geometric information carried by irregular and non-uniform non-Euclidean space. In order to address this issue, in this paper we propose a novel generic framework to learn the representation of spatial networks that are embedded in non-Euclidean manifold space. Specifically, a novel message-passing-based neural network is proposed to combine graph topology and spatial geometry, where spatial geometry is extracted as messages on the edges. We theoretically guarantee that the learned representations are provably invariant to important symmetries such as rotation or translation, and simultaneously maintain sufficient ability in distinguishing different geometric structures. The strength of our proposed method is demonstrated through extensive experiments on both synthetic and real-world datasets.

Effectively mining anomalous subgraphs in networks is crucial for many application scenarios, such as disease outbreak detection, financial fraud detection, and activity monitoring in social networks. Identifying anomalous subgraphs is extremely challenging due to their complex topological structures and high-dimensional attributes, various notions of anomalies, and the exponentially large subgraph space in a given graph. Existing classical shallow models typically rely on handcrafted anomaly measure functions, which cannot handle common situations when such prior knowledge is unavailable. Recently, deep learning-based methods provide an end-to-end way that learns the anomaly measure functions. However, although they have achieved great success in detecting node-level, edge-level, and graph-level anomalies, detecting anomalous at the subgraph level has been largely under-explored due to enormous difficulties in subgraph representation learning, supervision, and end-to-end anomaly quantification. To circumvent the above mentioned challenges, this paper proposes a novel deep framework named Anomalous Subgraph Autoencoder (AS-GAE) to extract the anomalous subgraphs in an unsupervised and weakly supervised manner. Specifically, we first develop a location-aware graph auto-encoder to uncover the anomalous areas in the given graph according to the mismatch during the reconstruction. Then a supermodular graph scoring function module is proposed to assign reasonable anomaly scores to the subgraphs in the extracted anomalous areas. The superiority of our proposed method was demonstrated through extensive experiments on two synthetic datasets and nine real-world datasets.