Convolutional neural networks (CNNs) have achieved remarkable performance in hyperspectral image (HSI) classification over the last few years. Despite the progress that has been made, rich and informative spectral information of HSI has been largely underutilized by existing methods which employ convolutional kernels with limited size of receptive field in the spectral domain. To address this issue, we propose a spectral graph reasoning network (SGR) learning framework comprising two crucial modules: 1) a spectral decoupling module which unpacks and casts multiple spectral embeddings into a unified graph whose node corresponds to an individual spectral feature channel in the embedding space; the graph performs interpretable reasoning to aggregate and align spectral information to guide learning spectral-specific graph embeddings at multiple contextual levels 2) a spectral ensembling module explores the interactions and interdependencies across graph embedding hierarchy via a novel recurrent graph propagation mechanism. Experiments on two HSI datasets demonstrate that the proposed architecture can significantly improve the classification accuracy compared with the existing methods with a sizable margin.
Knowledge Graph Embedding (KGE) is a common method for Knowledge Graphs (KGs) to serve various artificial intelligence tasks. The suitable dimensions of the embeddings depend on the storage and computing conditions of the specific application scenarios. Once a new dimension is required, a new KGE model needs to be trained from scratch, which greatly increases the training cost and limits the efficiency and flexibility of KGE in serving various scenarios. In this work, we propose a novel KGE training framework MED, through which we could train once to get a croppable KGE model applicable to multiple scenarios with different dimensional requirements, sub-models of the required dimensions can be cropped out of it and used directly without any additional training. In MED, we propose a mutual learning mechanism to improve the low-dimensional sub-models performance and make the high-dimensional sub-models retain the capacity that low-dimensional sub-models have, an evolutionary improvement mechanism to promote the high-dimensional sub-models to master the knowledge that the low-dimensional sub-models can not learn, and a dynamic loss weight to balance the multiple losses adaptively. Experiments on 3 KGE models over 4 standard KG completion datasets, 3 real application scenarios over a real-world large-scale KG, and the experiments of extending MED to the language model BERT show the effectiveness, high efficiency, and flexible extensibility of MED.
We developed DyGETViz, a novel framework for effectively visualizing dynamic graphs (DGs) that are ubiquitous across diverse real-world systems. This framework leverages recent advancements in discrete-time dynamic graph (DTDG) models to adeptly handle the temporal dynamics inherent in dynamic graphs. DyGETViz effectively captures both micro- and macro-level structural shifts within these graphs, offering a robust method for representing complex and massive dynamic graphs. The application of DyGETViz extends to a diverse array of domains, including ethology, epidemiology, finance, genetics, linguistics, communication studies, social studies, and international relations. Through its implementation, DyGETViz has revealed or confirmed various critical insights. These include the diversity of content sharing patterns and the degree of specialization within online communities, the chronological evolution of lexicons across decades, and the distinct trajectories exhibited by aging-related and non-related genes. Importantly, DyGETViz enhances the accessibility of scientific findings to non-domain experts by simplifying the complexities of dynamic graphs. Our framework is released as an open-source Python package for use across diverse disciplines. Our work not only addresses the ongoing challenges in visualizing and analyzing DTDG models but also establishes a foundational framework for future investigations into dynamic graph representation and analysis across various disciplines.
Click-through-rate (CTR) prediction has an essential impact on improving user experience and revenue in e-commerce search. With the development of deep learning, graph-based methods are well exploited to utilize graph structure extracted from user behaviors and other information to help embedding learning. However, most of the previous graph-based methods mainly focus on recommendation scenarios, and therefore their graph structures highly depend on item's sequential information from user behaviors, ignoring query's sequential signal and query-item correlation. In this paper, we propose a new approach named Light-weight End-to-End Graph Interest Network (EGIN) to effectively mine users' search interests and tackle previous challenges. (i) EGIN utilizes query and item's correlation and sequential information from the search system to build a heterogeneous graph for better CTR prediction in e-commerce search. (ii) EGIN's graph embedding learning shares the same training input and is jointly trained with CTR prediction, making the end-to-end framework effortless to deploy in large-scale search systems. The proposed EGIN is composed of three parts: query-item heterogeneous graph, light-weight graph sampling, and multi-interest network. The query-item heterogeneous graph captures correlation and sequential information of query and item efficiently by the proposed light-weight graph sampling. The multi-interest network is well designed to utilize graph embedding to capture various similarity relationships between query and item to enhance the final CTR prediction. We conduct extensive experiments on both public and industrial datasets to demonstrate the effectiveness of the proposed EGIN. At the same time, the training cost of graph learning is relatively low compared with the main CTR prediction task, ensuring efficiency in practical applications.
Recent studies successfully learned static graph embeddings that are structurally fair by preventing the effectiveness disparity of high- and low-degree vertex groups in downstream graph mining tasks. However, achieving structure fairness in dynamic graph embedding remains an open problem. Neglecting degree changes in dynamic graphs will significantly impair embedding effectiveness without notably improving structure fairness. This is because the embedding performance of high-degree and low-to-high-degree vertices will significantly drop close to the generally poorer embedding performance of most slightly changed vertices in the long-tail part of the power-law distribution. We first identify biased structural evolutions in a dynamic graph based on the evolving trend of vertex degree and then propose FairDGE, the first structurally Fair Dynamic Graph Embedding algorithm. FairDGE learns biased structural evolutions by jointly embedding the connection changes among vertices and the long-short-term evolutionary trend of vertex degrees. Furthermore, a novel dual debiasing approach is devised to encode fair embeddings contrastively, customizing debiasing strategies for different biased structural evolutions. This innovative debiasing strategy breaks the effectiveness bottleneck of embeddings without notable fairness loss. Extensive experiments demonstrate that FairDGE achieves simultaneous improvement in the effectiveness and fairness of embeddings.
Federated Knowledge Graphs Embedding learning (FKGE) encounters challenges in communication efficiency stemming from the considerable size of parameters and extensive communication rounds. However, existing FKGE methods only focus on reducing communication rounds by conducting multiple rounds of local training in each communication round, and ignore reducing the size of parameters transmitted within each communication round. To tackle the problem, we first find that universal reduction in embedding precision across all entities during compression can significantly impede convergence speed, underscoring the importance of maintaining embedding precision. We then propose bidirectional communication-efficient FedS based on Entity-Wise Top-K Sparsification strategy. During upload, clients dynamically identify and upload only the Top-K entity embeddings with the greater changes to the server. During download, the server first performs personalized embedding aggregation for each client. It then identifies and transmits the Top-K aggregated embeddings to each client. Besides, an Intermittent Synchronization Mechanism is used by FedS to mitigate negative effect of embedding inconsistency among shared entities of clients caused by heterogeneity of Federated Knowledge Graph. Extensive experiments across three datasets showcase that FedS significantly enhances communication efficiency with negligible (even no) performance degradation.
Representation learning on text-attributed graphs (TAGs), where nodes are represented by textual descriptions, is crucial for textual and relational knowledge systems and recommendation systems. Currently, state-of-the-art embedding methods for TAGs primarily focus on fine-tuning language models (e.g., BERT) using structure-aware training signals. While effective, these methods are tailored for individual TAG and cannot generalize across various graph scenarios. Given the shared textual space, leveraging multiple TAGs for joint fine-tuning, aligning text and graph structure from different aspects, would be more beneficial. Motivated by this, we introduce a novel Unified Graph Language Model (UniGLM) framework, the first graph embedding model that generalizes well to both in-domain and cross-domain TAGs. Specifically, UniGLM is trained over multiple TAGs with different domains and scales using self-supervised contrastive learning. UniGLM includes an adaptive positive sample selection technique for identifying structurally similar nodes and a lazy contrastive module that is devised to accelerate training by minimizing repetitive encoding calculations. Extensive empirical results across 9 benchmark TAGs demonstrate UniGLM's efficacy against leading embedding baselines in terms of generalization (various downstream tasks and backbones) and transfer learning (in and out of domain scenarios). The code is available at https://github.com/NYUSHCS/UniGLM.
Federated Knowledge Graph Embedding (FKGE) has recently garnered considerable interest due to its capacity to extract expressive representations from distributed knowledge graphs, while concurrently safeguarding the privacy of individual clients. Existing FKGE methods typically harness the arithmetic mean of entity embeddings from all clients as the global supplementary knowledge, and learn a replica of global consensus entities embeddings for each client. However, these methods usually neglect the inherent semantic disparities among distinct clients. This oversight not only results in the globally shared complementary knowledge being inundated with too much noise when tailored to a specific client, but also instigates a discrepancy between local and global optimization objectives. Consequently, the quality of the learned embeddings is compromised. To address this, we propose Personalized Federated knowledge graph Embedding with client-wise relation Graph (PFedEG), a novel approach that employs a client-wise relation graph to learn personalized embeddings by discerning the semantic relevance of embeddings from other clients. Specifically, PFedEG learns personalized supplementary knowledge for each client by amalgamating entity embedding from its neighboring clients based on their "affinity" on the client-wise relation graph. Each client then conducts personalized embedding learning based on its local triples and personalized supplementary knowledge. We conduct extensive experiments on four benchmark datasets to evaluate our method against state-of-the-art models and results demonstrate the superiority of our method.
Multi-agent path finding (MAPF) is the problem of finding paths for multiple agents such that they do not collide. This problem manifests in numerous real-world applications such as controlling transportation robots in automated warehouses, moving characters in video games, and coordinating self-driving cars in intersections. Finding optimal solutions to MAPF is NP-Hard, yet modern optimal solvers can scale to hundreds of agents and even thousands in some cases. Different solvers employ different approaches, and there is no single state-of-the-art approach for all problems. Furthermore, there are no clear, provable, guidelines for choosing when each optimal MAPF solver to use. Prior work employed Algorithm Selection (AS) techniques to learn such guidelines from past data. A major challenge when employing AS for choosing an optimal MAPF algorithm is how to encode the given MAPF problem. Prior work either used hand-crafted features or an image representation of the problem. We explore graph-based encodings of the MAPF problem and show how they can be used on-the-fly with a modern graph embedding algorithm called FEATHER. Then, we show how this encoding can be effectively joined with existing encodings, resulting in a novel AS method we call MAPF Algorithm selection via Graph embedding (MAG). An extensive experimental evaluation of MAG on several MAPF algorithm selection tasks reveals that it is either on-par or significantly better than existing methods.
Current directed graph embedding methods build upon undirected techniques but often inadequately capture directed edge information, leading to challenges such as: (1) Suboptimal representations for nodes with low in/out-degrees, due to the insufficient neighbor interactions; (2) Limited inductive ability for representing new nodes post-training; (3) Narrow generalizability, as training is overly coupled with specific tasks. In response, we propose DUPLEX, an inductive framework for complex embeddings of directed graphs. It (1) leverages Hermitian adjacency matrix decomposition for comprehensive neighbor integration, (2) employs a dual GAT encoder for directional neighbor modeling, and (3) features two parameter-free decoders to decouple training from particular tasks. DUPLEX outperforms state-of-the-art models, especially for nodes with sparse connectivity, and demonstrates robust inductive capability and adaptability across various tasks. The code is available at https://github.com/alipay/DUPLEX.
Graph is a ubiquitous representation of data in various research fields, and graph embedding is a prevalent machine learning technique for capturing key features and generating fixed-sized attributes. However, most state-of-the-art graph embedding methods are computationally and spatially expensive. Recently, the Graph Encoder Embedding (GEE) has been shown as the fastest graph embedding technique and is suitable for a variety of network data applications. As real-world data often involves large and sparse graphs, the huge sparsity usually results in redundant computations and storage. To address this issue, we propose an improved version of GEE, sparse GEE, which optimizes the calculation and storage of zero entries in sparse matrices to enhance the running time further. Our experiments demonstrate that the sparse version achieves significant speedup compared to the original GEE with Python implementation for large sparse graphs, and sparse GEE is capable of processing millions of edges within minutes on a standard laptop.
While there are a plethora of methods for link prediction in knowledge graphs, state-of-the-art approaches are often black box, obfuscating model reasoning and thereby limiting the ability of users to make informed decisions about model predictions. Recently, methods have emerged to generate prediction explanations for Knowledge Graph Embedding models, a widely-used class of methods for link prediction. The question then becomes, how well do these explanation systems work? To date this has generally been addressed anecdotally, or through time-consuming user research. In this work, we present an in-depth exploration of a simple link prediction explanation method we call LinkLogic, that surfaces and ranks explanatory information used for the prediction. Importantly, we construct the first-ever link prediction explanation benchmark, based on family structures present in the FB13 dataset. We demonstrate the use of this benchmark as a rich evaluation sandbox, probing LinkLogic quantitatively and qualitatively to assess the fidelity, selectivity and relevance of the generated explanations. We hope our work paves the way for more holistic and empirical assessment of knowledge graph prediction explanation methods in the future.
Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on spectral graph wavelets that employs a contrastive learning approach. We theoretically show that in Paley-Wiener spaces on combinatorial graphs, the spectral graph wavelets operator provides greater flexibility and control over smoothness compared to the Laplacian operator, motivating our approach. An additional key advantage of the proposed embedding is its ability to establish a correspondence between the embedding and input feature spaces, enabling the derivation of feature importance. We validate the effectiveness of our graph embedding framework on multiple public datasets across various downstream tasks, including clustering and unsupervised feature importance.
In recent years, graph neural networks (GNNs) have become increasingly popular for solving NP-hard combinatorial optimization (CO) problems, such as maximum cut and maximum independent set. The core idea behind these methods is to represent a CO problem as a graph and then use GNNs to learn the node/graph embedding with combinatorial information. Although these methods have achieved promising results, given a specific CO problem, the design of GNN architectures still requires heavy manual work with domain knowledge. Existing automated GNNs are mostly focused on traditional graph learning problems, which is inapplicable to solving NP-hard CO problems. To this end, we present a new class of \textbf{AUTO}mated \textbf{G}NNs for solving \textbf{NP}-hard problems, namely \textbf{AutoGNP}. We represent CO problems by GNNs and focus on two specific problems, i.e., mixed integer linear programming and quadratic unconstrained binary optimization. The idea of AutoGNP is to use graph neural architecture search algorithms to automatically find the best GNNs for a given NP-hard combinatorial optimization problem. Compared with existing graph neural architecture search algorithms, AutoGNP utilizes two-hop operators in the architecture search space. Moreover, AutoGNP utilizes simulated annealing and a strict early stopping policy to avoid local optimal solutions. Empirical results on benchmark combinatorial problems demonstrate the superiority of our proposed model.
This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding, and seamlessly integrates multiple kernels to enhance the learning process. Our theoretical analysis offers a population-level characterization of this approach using random variables. Empirically, our method demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network, while achieving comparable classification accuracy across various simulated and real datasets.
While Multi-view Graph Neural Networks (MVGNNs) excel at leveraging diverse modalities for learning object representation, existing methods assume identical local topology structures across modalities that overlook real-world discrepancies. This leads MVGNNs straggles in modality fusion and representations denoising. To address these issues, we propose adaptive modality-wise structure learning (AMoSL). AMoSL captures node correspondences between modalities via optimal transport, and jointly learning with graph embedding. To enable efficient end-to-end training, we employ an efficient solution for the resulting complex bilevel optimization problem. Furthermore, AMoSL adapts to downstream tasks through unsupervised learning on inter-modality distances. The effectiveness of AMoSL is demonstrated by its ability to train more accurate graph classifiers on six benchmark datasets.
In this paper, we introduce a post-hoc and local explainable AI method tailored for Knowledge Graph Embedding (KGE) models. These models are essential to Knowledge Graph Completion yet criticized for their opaque, black-box nature. Despite their significant success in capturing the semantics of knowledge graphs through high-dimensional latent representations, their inherent complexity poses substantial challenges to explainability. While existing methods like Kelpie use resource-intensive perturbation to explain KGE models, our approach directly decodes the latent representations encoded by KGE models, leveraging the smoothness of the embeddings, which follows the principle that similar embeddings reflect similar behaviours within the Knowledge Graph, meaning that nodes are similarly embedded because their graph neighbourhood looks similar. This principle is commonly referred to as smoothness. By identifying symbolic structures, in the form of triples, within the subgraph neighborhoods of similarly embedded entities, our method identifies the statistical regularities on which the models rely and translates these insights into human-understandable symbolic rules and facts. This bridges the gap between the abstract representations of KGE models and their predictive outputs, offering clear, interpretable insights. Key contributions include a novel post-hoc and local explainable AI method for KGE models that provides immediate, faithful explanations without retraining, facilitating real-time application on large-scale knowledge graphs. The method's flexibility enables the generation of rule-based, instance-based, and analogy-based explanations, meeting diverse user needs. Extensive evaluations show the effectiveness of our approach in delivering faithful and well-localized explanations, enhancing the transparency and trustworthiness of KGE models.
Identifiability of statistical models is a key notion in unsupervised representation learning. Recent work of nonlinear independent component analysis (ICA) employs auxiliary data and has established identifiable conditions. This paper proposes a statistical model of two latent vectors with single auxiliary data generalizing nonlinear ICA, and establishes various identifiability conditions. Unlike previous work, the two latent vectors in the proposed model can have arbitrary dimensions, and this property enables us to reveal an insightful dimensionality relation among two latent vectors and auxiliary data in identifiability conditions. Furthermore, surprisingly, we prove that the indeterminacies of the proposed model has the same as \emph{linear} ICA under certain conditions: The elements in the latent vector can be recovered up to their permutation and scales. Next, we apply the identifiability theory to a statistical model for graph data. As a result, one of the identifiability conditions includes an appealing implication: Identifiability of the statistical model could depend on the maximum value of link weights in graph data. Then, we propose a practical method for identifiable graph embedding. Finally, we numerically demonstrate that the proposed method well-recovers the latent vectors and model identifiability clearly depends on the maximum value of link weights, which supports the implication of our theoretical results
Personalized subgraph Federated Learning (FL) is a task that customizes Graph Neural Networks (GNNs) to individual client needs, accommodating diverse data distributions. However, applying hypernetworks in FL, while aiming to facilitate model personalization, often encounters challenges due to inadequate representation of client-specific characteristics. To overcome these limitations, we propose a model called FedSheafHN, using enhanced collaboration graph embedding and efficient personalized model parameter generation. Specifically, our model embeds each client's local subgraph into a server-constructed collaboration graph. We utilize sheaf diffusion in the collaboration graph to learn client representations. Our model improves the integration and interpretation of complex client characteristics. Furthermore, our model ensures the generation of personalized models through advanced hypernetworks optimized for parallel operations across clients. Empirical evaluations demonstrate that FedSheafHN outperforms existing methods in most scenarios, in terms of client model performance on various graph-structured datasets. It also has fast model convergence and effective new clients generalization.
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and inference on these systems, but getting a handle on uncertainty, especially in dynamic settings, is a challenging problem. In this work we propose to use a dynamic graph representation known in the tensor literature as the unfolding, to achieve valid prediction sets via conformal prediction. This representation, a simple graph, can be input to any standard GNN and does not require any modification to existing GNN architectures or conformal prediction routines. One of our key contributions is a careful mathematical consideration of the different inference scenarios which can arise in a dynamic graph modelling context. For a range of practically relevant cases, we obtain valid prediction sets with almost no assumptions, even dispensing with exchangeability. In a more challenging scenario, which we call the semi-inductive regime, we achieve valid prediction under stronger assumptions, akin to stationarity. We provide real data examples demonstrating validity, showing improved accuracy over baselines, and sign-posting different failure modes which can occur when those assumptions are violated.