Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the topology of the input graph. To resolve this we introduce a topological loss term to be added to the training loss of Node2vec which tries to align the persistence diagram (PD) of the resulting embedding as closely as possible to that of the input graph. Following results in computational optimal transport, we carefully adapt entropic regularization to PD metrics, allowing us to measure the discrepancy between PDs in a differentiable way. Our modified loss function can then be minimized through gradient descent to reconstruct both the geometry and the topology of the input graph. We showcase the benefits of this approach using demonstrative synthetic examples.
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis tasks like node classification, link prediction, and visualization. In this paper, we propose a novel force-directed graph embedding method that utilizes the steady acceleration kinetic formula to embed nodes in a way that preserves graph topology and structural features. Our method simulates a set of customized attractive and repulsive forces between all node pairs with respect to their hop distance. These forces are then used in Newton's second law to obtain the acceleration of each node. The method is intuitive, parallelizable, and highly scalable. We evaluate our method on several graph analysis tasks and show that it achieves competitive performance compared to state-of-the-art unsupervised embedding techniques.
Knowledge graph (KG) embedding has been used to benefit the diagnosis of animal diseases by analyzing electronic medical records (EMRs), such as notes and veterinary records. However, learning representations to capture entities and relations with literal information in KGs is challenging as the KGs show heterogeneous properties and various types of literal information. Meanwhile, the existing methods mostly aim to preserve graph structures surrounding target nodes without considering different types of literals, which could also carry significant information. In this paper, we propose a knowledge graph embedding model for the efficient diagnosis of animal diseases, which could learn various types of literal information and graph structure and fuse them into unified representations, namely LiteralKG. Specifically, we construct a knowledge graph that is built from EMRs along with literal information collected from various animal hospitals. We then fuse different types of entities and node feature information into unified vector representations through gate networks. Finally, we propose a self-supervised learning task to learn graph structure in pretext tasks and then towards various downstream tasks. Experimental results on link prediction tasks demonstrate that our model outperforms the baselines that consist of state-of-the-art models. The source code is available at https://github.com/NSLab-CUK/LiteralKG.
Drug repositioning-a promising strategy for discovering new therapeutic uses for existing drugs-has been increasingly explored in the computational science literature using biomedical databases. However, the technological potential of drug repositioning candidates has often been overlooked. This study presents a novel protocol to comprehensively analyse various sources such as pharmaceutical patents and biomedical databases, and identify drug repositioning candidates with both technological potential and scientific evidence. To this end, first, we constructed a scientific biomedical knowledge graph (s-BKG) comprising relationships between drugs, diseases, and genes derived from biomedical databases. Our protocol involves identifying drugs that exhibit limited association with the target disease but are closely located in the s-BKG, as potential drug candidates. We constructed a patent-informed biomedical knowledge graph (p-BKG) by adding pharmaceutical patent information. Finally, we developed a graph embedding protocol to ascertain the structure of the p-BKG, thereby calculating the relevance scores of those candidates with target disease-related patents to evaluate their technological potential. Our case study on Alzheimer's disease demonstrates its efficacy and feasibility, while the quantitative outcomes and systematic methods are expected to bridge the gap between computational discoveries and successful market applications in drug repositioning research.
Many downstream inference tasks for knowledge graphs, such as relation prediction, have been handled successfully by knowledge graph embedding techniques in the transductive setting. To address the inductive setting wherein new entities are introduced into the knowledge graph at inference time, more recent work opts for models which learn implicit representations of the knowledge graph through a complex function of a network's subgraph structure, often parametrized by graph neural network architectures. These come at the cost of increased parametrization, reduced interpretability and limited generalization to other downstream inference tasks. In this work, we bridge the gap between traditional transductive knowledge graph embedding approaches and more recent inductive relation prediction models by introducing a generalized form of harmonic extension which leverages representations learned through transductive embedding methods to infer representations of new entities introduced at inference time as in the inductive setting. This harmonic extension technique provides the best such approximation, can be implemented via an efficient iterative scheme, and can be employed to answer a family of conjunctive logical queries over the knowledge graph, further expanding the capabilities of transductive embedding methods. In experiments on a number of large-scale knowledge graph embedding benchmarks, we find that this approach for extending the functionality of transductive knowledge graph embedding models to perform knowledge graph completion and answer logical queries in the inductive setting is competitive with--and in some scenarios outperforms--several state-of-the-art models derived explicitly for such inductive tasks.
We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.
Temporal Interaction Graphs (TIGs) are widely employed to model intricate real-world systems such as financial systems and social networks. To capture the dynamism and interdependencies of nodes, existing TIG embedding models need to process edges sequentially and chronologically. However, this requirement prevents it from being processed in parallel and struggle to accommodate burgeoning data volumes to GPU. Consequently, many large-scale temporal interaction graphs are confined to CPU processing. Furthermore, a generalized GPU scaling and acceleration approach remains unavailable. To facilitate large-scale TIGs' implementation on GPUs for acceleration, we introduce a novel training approach namely Streaming Edge Partitioning and Parallel Acceleration for Temporal Interaction Graph Embedding (SPEED). The SPEED is comprised of a Streaming Edge Partitioning Component (SEP) which addresses space overhead issue by assigning fewer nodes to each GPU, and a Parallel Acceleration Component (PAC) which enables simultaneous training of different sub-graphs, addressing time overhead issue. Our method can achieve a good balance in computing resources, computing time, and downstream task performance. Empirical validation across 7 real-world datasets demonstrates the potential to expedite training speeds by a factor of up to 19.29x. Simultaneously, resource consumption of a single-GPU can be diminished by up to 69%, thus enabling the multiple GPU-based training and acceleration encompassing millions of nodes and billions of edges. Furthermore, our approach also maintains its competitiveness in downstream tasks.
Pain is a complex concept that can interconnect with other concepts such as a disorder that might cause pain, a medication that might relieve pain, and so on. To fully understand the context of pain experienced by either an individual or across a population, we may need to examine all concepts related to pain and the relationships between them. This is especially useful when modeling pain that has been recorded in electronic health records. Knowledge graphs represent concepts and their relations by an interlinked network, enabling semantic and context-based reasoning in a computationally tractable form. These graphs can, however, be too large for efficient computation. Knowledge graph embeddings help to resolve this by representing the graphs in a low-dimensional vector space. These embeddings can then be used in various downstream tasks such as classification and link prediction. The various relations associated with pain which are required to construct such a knowledge graph can be obtained from external medical knowledge bases such as SNOMED CT, a hierarchical systematic nomenclature of medical terms. A knowledge graph built in this way could be further enriched with real-world examples of pain and its relations extracted from electronic health records. This paper describes the construction of such knowledge graph embedding models of pain concepts, extracted from the unstructured text of mental health electronic health records, combined with external knowledge created from relations described in SNOMED CT, and their evaluation on a subject-object link prediction task. The performance of the models was compared with other baseline models.
Learning graph embeddings is a crucial task in graph mining tasks. An effective graph embedding model can learn low-dimensional representations from graph-structured data for data publishing benefiting various downstream applications such as node classification, link prediction, etc. However, recent studies have revealed that graph embeddings are susceptible to attribute inference attacks, which allow attackers to infer private node attributes from the learned graph embeddings. To address these concerns, privacy-preserving graph embedding methods have emerged, aiming to simultaneously consider primary learning and privacy protection through adversarial learning. However, most existing methods assume that representation models have access to all sensitive attributes in advance during the training stage, which is not always the case due to diverse privacy preferences. Furthermore, the commonly used adversarial learning technique in privacy-preserving representation learning suffers from unstable training issues. In this paper, we propose a novel approach called Private Variational Graph AutoEncoders (PVGAE) with the aid of independent distribution penalty as a regularization term. Specifically, we split the original variational graph autoencoder (VGAE) to learn sensitive and non-sensitive latent representations using two sets of encoders. Additionally, we introduce a novel regularization to enforce the independence of the encoders. We prove the theoretical effectiveness of regularization from the perspective of mutual information. Experimental results on three real-world datasets demonstrate that PVGAE outperforms other baselines in private embedding learning regarding utility performance and privacy protection.
Knowledge Graph Embedding (KGE) has proven to be an effective approach to solving the Knowledge Graph Completion (KGC) task. Relational patterns which refer to relations with specific semantics exhibiting graph patterns are an important factor in the performance of KGE models. Though KGE models' capabilities are analyzed over different relational patterns in theory and a rough connection between better relational patterns modeling and better performance of KGC has been built, a comprehensive quantitative analysis on KGE models over relational patterns remains absent so it is uncertain how the theoretical support of KGE to a relational pattern contributes to the performance of triples associated to such a relational pattern. To address this challenge, we evaluate the performance of 7 KGE models over 4 common relational patterns on 2 benchmarks, then conduct an analysis in theory, entity frequency, and part-to-whole three aspects and get some counterintuitive conclusions. Finally, we introduce a training-free method Score-based Patterns Adaptation (SPA) to enhance KGE models' performance over various relational patterns. This approach is simple yet effective and can be applied to KGE models without additional training. Our experimental results demonstrate that our method generally enhances performance over specific relational patterns. Our source code is available from GitHub at https://github.com/zjukg/Comprehensive-Study-over-Relational-Patterns.
A knowledge graph is a powerful representation of real-world entities and their relations. The vast majority of these relations are defined as positive statements, but the importance of negative statements is increasingly recognized, especially under an Open World Assumption. Explicitly considering negative statements has been shown to improve performance on tasks such as entity summarization and question answering or domain-specific tasks such as protein function prediction. However, no attention has been given to the exploration of negative statements by knowledge graph embedding approaches despite the potential of negative statements to produce more accurate representations of entities in a knowledge graph. We propose a novel approach, TrueWalks, to incorporate negative statements into the knowledge graph representation learning process. In particular, we present a novel walk-generation method that is able to not only differentiate between positive and negative statements but also take into account the semantic implications of negation in ontology-rich knowledge graphs. This is of particular importance for applications in the biomedical domain, where the inadequacy of embedding approaches regarding negative statements at the ontology level has been identified as a crucial limitation. We evaluate TrueWalks in ontology-rich biomedical knowledge graphs in two different predictive tasks based on KG embeddings: protein-protein interaction prediction and gene-disease association prediction. We conduct an extensive analysis over established benchmarks and demonstrate that our method is able to improve the performance of knowledge graph embeddings on all tasks.
The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.
Knowledge graph embedding (KGE) focuses on representing the entities and relations of a knowledge graph (KG) into the continuous vector spaces, which can be employed to predict the missing triples to achieve knowledge graph completion (KGC). However, KGE models often only briefly learn structural correlations of triple data and embeddings would be misled by the trivial patterns and noisy links in real-world KGs. To address this issue, we build the new paradigm of KGE in the context of causality and embedding disentanglement. We further propose a Causality-enhanced knowledge graph Embedding (CausE) framework. CausE employs causal intervention to estimate the causal effect of the confounder embeddings and design new training objectives to make stable predictions. Experimental results demonstrate that CausE could outperform the baseline models and achieve state-of-the-art KGC performance. We release our code in https://github.com/zjukg/CausE.
The domain of machine learning is confronted with a crucial research area known as class imbalance learning, which presents considerable hurdles in precise classification of minority classes. This issue can result in biased models where the majority class takes precedence in the training process, leading to the underrepresentation of the minority class. The random vector functional link (RVFL) network is a widely used and effective learning model for classification due to its good generalization performance and efficiency. However, it suffers when dealing with imbalanced datasets. To overcome this limitation, we propose a novel graph embedded intuitionistic fuzzy RVFL for class imbalance learning (GE-IFRVFL-CIL) model incorporating a weighting mechanism to handle imbalanced datasets. The proposed GE-IFRVFL-CIL model offers plethora of benefits: $(i)$ leveraging graph embedding to preserve the inherent topological structure of the datasets, $(ii)$ employing intuitionistic fuzzy theory to handle uncertainty and imprecision in the data, $(iii)$ and the most important, it tackles class imbalance learning. The amalgamation of a weighting scheme, graph embedding, and intuitionistic fuzzy sets leads to the superior performance of the proposed models on KEEL benchmark imbalanced datasets with and without Gaussian noise. Furthermore, we implemented the proposed GE-IFRVFL-CIL on the ADNI dataset and achieved promising results, demonstrating the model's effectiveness in real-world applications. The proposed GE-IFRVFL-CIL model offers a promising solution to address the class imbalance issue, mitigates the detrimental effect of noise and outliers, and preserves the inherent geometrical structures of the dataset.
A wide variety of generative models for graphs have been proposed. They are used in drug discovery, road networks, neural architecture search, and program synthesis. Generating graphs has theoretical challenges, such as isomorphic representations -- evaluating how well a generative model performs is difficult. Which model to choose depending on the application domain? We extensively study kernel-based metrics on distributions of graph invariants and manifold-based and kernel-based metrics in graph embedding space. Manifold-based metrics outperform kernel-based metrics in embedding space. We use these metrics to compare GraphRNN and GRAN, two well-known generative models for graphs, and unveil the influence of node orderings. It shows the superiority of GRAN over GraphRNN - further, our proposed adaptation of GraphRNN with a depth-first search ordering is effective for small-sized graphs. A guideline on good practices regarding dataset selection and node feature initialization is provided. Our work is accompanied by open-source code and reproducible experiments.
Knowledge Graph Embedding (KGE) models are used to learn continuous representations of entities and relations. A key task in the literature is predicting missing links between entities. However, Knowledge Graphs are not just sets of links but also have semantics underlying their structure. Semantics is crucial in several downstream tasks, such as query answering or reasoning. We introduce the subgraph inference task, where a model has to generate likely and semantically valid subgraphs. We propose IntelliGraphs, a set of five new Knowledge Graph datasets. The IntelliGraphs datasets contain subgraphs with semantics expressed in logical rules for evaluating subgraph inference. We also present the dataset generator that produced the synthetic datasets. We designed four novel baseline models, which include three models based on traditional KGEs. We evaluate their expressiveness and show that these models cannot capture the semantics. We believe this benchmark will encourage the development of machine learning models that emphasize semantic understanding.
In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited capacity in representing graphs of varying structures. A promising candidate for the faithful embedding of data with varying structure is product manifolds of component spaces of different geometries (spherical, hyperbolic, or euclidean). In this paper, we take a closer look at the structure of product manifold embedding spaces and argue that each component space in a product contributes differently to expressing structures in the input graph, hence should be weighted accordingly. This is different from previous works which consider the roles of different components equally. We then propose WEIGHTED-PM, a data-driven method for learning embedding of heterogeneous graphs in weighted product manifolds. Our method utilizes the topological information of the input graph to automatically determine the weight of each component in product spaces. Extensive experiments on synthetic and real-world graph datasets demonstrate that WEIGHTED-PM is capable of learning better graph representations with lower geometric distortion from input data, and performs better on multiple downstream tasks, such as word similarity learning, top-$k$ recommendation, and knowledge graph embedding.
Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state ($t$) and previous context (over timestamps [$t-1, t-l$], $l$ is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp $t$. We consider diverse benchmarks with varying levels of ``novelty" as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.
Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture long-range dependencies and global patterns in graphs. To address this, we propose a new inductive bias based on variational analysis, drawing inspiration from the Brachistochrone problem. Our framework establishes a mapping between discrete GNN models and continuous diffusion functionals. This enables the design of application-specific objective functions in the continuous domain and the construction of discrete deep models with mathematical guarantees. To tackle over-smoothing in GNNs, we analyze the existing layer-by-layer graph embedding models and identify that they are equivalent to l2-norm integral functionals of graph gradients, which cause over-smoothing. Similar to edge-preserving filters in image denoising, we introduce total variation (TV) to align the graph diffusion pattern with global community topologies. Additionally, we devise a selective mechanism to address the trade-off between model depth and over-smoothing, which can be easily integrated into existing GNNs. Furthermore, we propose a novel generative adversarial network (GAN) that predicts spreading flows in graphs through a neural transport equation. To mitigate vanishing flows, we customize the objective function to minimize transportation within each community while maximizing inter-community flows. Our GNN models achieve state-of-the-art (SOTA) performance on popular graph learning benchmarks such as Cora, Citeseer, and Pubmed.
This paper presents a translation-based knowledge geraph embedding method via efficient relation rotation (TransERR), a straightforward yet effective alternative to traditional translation-based knowledge graph embedding models. Different from the previous translation-based models, TransERR encodes knowledge graphs in the hypercomplex-valued space, thus enabling it to possess a higher degree of translation freedom in mining latent information between the head and tail entities. To further minimize the translation distance, TransERR adaptively rotates the head entity and the tail entity with their corresponding unit quaternions, which are learnable in model training. We also provide mathematical proofs to demonstrate the ability of TransERR in modeling various relation patterns, including symmetry, antisymmetry, inversion, composition, and subrelation patterns. The experiments on 10 benchmark datasets validate the effectiveness and the generalization of TransERR. The results also indicate that TransERR can better encode large-scale datasets with fewer parameters than the previous translation-based models. Our code and datasets are available at~\url{https://github.com/dellixx/TransERR}.