AI-driven drug design relies significantly on predicting molecular properties, which is a complex task. In current approaches, the most commonly used feature representations for training deep neural network models are based on SMILES and molecular graphs. While these methods are concise and efficient, they have limitations in capturing complex spatial information. Recently, researchers have recognized the importance of incorporating three-dimensional information of molecular structures into models. However, capturing spatial information requires the introduction of additional units in the generator, bringing additional design and computational costs. Therefore, it is necessary to develop a method for predicting molecular properties that effectively combines spatial structural information while maintaining the simplicity and efficiency of graph neural networks. In this work, we propose an embedding approach CTAGE, utilizing $k$-hop discrete Ricci curvature to extract structural insights from molecular graph data. This effectively integrates spatial structural information while preserving the training complexity of the network. Experimental results indicate that introducing node curvature significantly improves the performance of current graph neural network frameworks, validating that the information from k-hop node curvature effectively reflects the relationship between molecular structure and function.
Knowledge graphs can be used in many areas related to data semantics such as question-answering systems, knowledge based systems. However, the currently constructed knowledge graphs need to be complemented for better knowledge in terms of relations. It is called knowledge graph completion. To add new relations to the existing knowledge graph by using knowledge graph embedding models, we have to evaluate $N\times N \times R$ vector operations, where $N$ is the number of entities and $R$ is the number of relation types. It is very costly. In this paper, we provide an efficient knowledge graph completion framework on GPUs to get new relations using knowledge graph embedding vectors. In the proposed framework, we first define "transformable to a metric space" and then provide a method to transform the knowledge graph completion problem into the similarity join problem for a model which is "transformable to a metric space". After that, to efficiently process the similarity join problem, we derive formulas using the properties of a metric space. Based on the formulas, we develop a fast knowledge graph completion algorithm. Finally, we experimentally show that our framework can efficiently process the knowledge graph completion problem.
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.
Heterogeneous information networks (HINs) have been extensively applied to real-world tasks, such as recommendation systems, social networks, and citation networks. While existing HIN representation learning methods can effectively learn the semantic and structural features in the network, little awareness was given to the distribution discrepancy of subgraphs within a single HIN. However, we find that ignoring such distribution discrepancy among subgraphs from multiple sources would hinder the effectiveness of graph embedding learning algorithms. This motivates us to propose SUMSHINE (Scalable Unsupervised Multi-Source Heterogeneous Information Network Embedding) -- a scalable unsupervised framework to align the embedding distributions among multiple sources of an HIN. Experimental results on real-world datasets in a variety of downstream tasks validate the performance of our method over the state-of-the-art heterogeneous information network embedding algorithms.
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.
Over the years, many frameworks and optimization techniques have been proposed to accelerate graph neural networks (GNNs). Compared to the optimizations explored in these systems, we observe that different matrix re-associations of GNN computations lead to novel input-sensitive performance behavior. We leverage this observation to propose SENSEi, a system that exposes different sparse and dense matrix primitive compositions based on different matrix re-associations of GNN computations and selects the best among them based on input attributes. SENSEi executes in two stages: (1) an offline compilation stage that enumerates all valid re-associations leading to different sparse-dense matrix compositions and uses input-oblivious pruning techniques to prune away clearly unprofitable candidates and (2) an online runtime system that explores the remaining candidates and uses light-weight cost models to select the best re-association based on the input graph and the embedding sizes on a given hardware platform. On a wide range of configurations, SENSEi achieves speedups of up to $2.012\times$ and $1.85\times$ on graph convolutional networks and up to $6.294\times$ and $16.274\times$ on graph attention networks, on GPUs and CPUs respectively. We also show that its technique generalizes to GNN variants, including those that require sampling. Furthermore, we show that SENSEi's techniques are agnostic to the underlying GNN system, and can be used to yield synergistic improvements across a diverse set of implementations.
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}.
The proliferation of open knowledge graphs has led to a surge in scholarly research on the topic over the past decade. This paper presents a bibliometric analysis of the scholarly literature on open knowledge graphs published between 2013 and 2023. The study aims to identify the trends, patterns, and impact of research in this field, as well as the key topics and research questions that have emerged. The work uses bibliometric techniques to analyze a sample of 4445 scholarly articles retrieved from Scopus. The findings reveal an ever-increasing number of publications on open knowledge graphs published every year, particularly in developed countries (+50 per year). These outputs are published in highly-referred scholarly journals and conferences. The study identifies three main research themes: (1) knowledge graph construction and enrichment, (2) evaluation and reuse, and (3) fusion of knowledge graphs into NLP systems. Within these themes, the study identifies specific tasks that have received considerable attention, including entity linking, knowledge graph embedding, and graph neural networks.
Graph Representation Learning (GRL) is an influential methodology, enabling a more profound understanding of graph-structured data and aiding graph clustering, a critical task across various domains. The recent incursion of attention mechanisms, originally an artifact of Natural Language Processing (NLP), into the realm of graph learning has spearheaded a notable shift in research trends. Consequently, Graph Attention Networks (GATs) and Graph Attention Auto-Encoders have emerged as preferred tools for graph clustering tasks. Yet, these methods primarily employ a local attention mechanism, thereby curbing their capacity to apprehend the intricate global dependencies between nodes within graphs. Addressing these impediments, this study introduces an innovative method known as the Graph Transformer Auto-Encoder for Graph Clustering (GTAGC). By melding the Graph Auto-Encoder with the Graph Transformer, GTAGC is adept at capturing global dependencies between nodes. This integration amplifies the graph representation and surmounts the constraints posed by the local attention mechanism. The architecture of GTAGC encompasses graph embedding, integration of the Graph Transformer within the autoencoder structure, and a clustering component. It strategically alternates between graph embedding and clustering, thereby tailoring the Graph Transformer for clustering tasks, whilst preserving the graph's global structural information. Through extensive experimentation on diverse benchmark datasets, GTAGC has exhibited superior performance against existing state-of-the-art graph clustering methodologies.
This work proposes a Physics-informed Neural Network framework with Graph Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of traditional Euclidean space, for improved problem-solving efficiency. The method integrates topological data into the neural network's computations, which significantly boosts the performance of the Physics-Informed Neural Network (PINN). The graph embedding technique infuses extra dimensions into the input space to encapsulate the spatial characteristics of a graph while preserving the properties of the original space. The selection of these extra dimensions is guided by the Fiedler vector, offering an optimised pathologic notation of the graph. Two case studies are conducted, which demonstrate significant improvement in the performance of GPINN in comparison to traditional PINN, particularly in its superior ability to capture physical features of the solution.
Knowledge graph completion (KGC) aims to solve the incompleteness of knowledge graphs (KGs) by predicting missing links from known triples, numbers of knowledge graph embedding (KGE) models have been proposed to perform KGC by learning embeddings. Nevertheless, most existing embedding models map each relation into a unique vector, overlooking the specific fine-grained semantics of them under different entities. Additionally, the few available fine-grained semantic models rely on clustering algorithms, resulting in limited performance and applicability due to the cumbersome two-stage training process. In this paper, we present a novel method utilizing contextual dictionary lookup, enabling conventional embedding models to learn fine-grained semantics of relations in an end-to-end manner. More specifically, we represent each relation using a dictionary that contains multiple latent semantics. The composition of a given entity and the dictionary's central semantics serves as the context for generating a lookup, thus determining the fine-grained semantics of the relation adaptively. The proposed loss function optimizes both the central and fine-grained semantics simultaneously to ensure their semantic consistency. Besides, we introduce two metrics to assess the validity and accuracy of the dictionary lookup operation. We extend several KGE models with the method, resulting in substantial performance improvements on widely-used benchmark datasets.
Conventional time series classification approaches based on bags of patterns or shapelets face significant challenges in dealing with a vast amount of feature candidates from high-dimensional multivariate data. In contrast, deep neural networks can learn low-dimensional features efficiently, and in particular, Convolutional Neural Networks (CNN) have shown promising results in classifying Multivariate Time Series (MTS) data. A key factor in the success of deep neural networks is this astonishing expressive power. However, this power comes at the cost of complex, black-boxed models, conflicting with the goals of building reliable and human-understandable models. An essential criterion in understanding such predictive deep models involves quantifying the contribution of time-varying input variables to the classification. Hence, in this work, we introduce a new framework for interpreting multivariate time series data by extracting and clustering the input representative patterns that highly activate CNN neurons. This way, we identify each signal's role and dependencies, considering all possible combinations of signals in the MTS input. Then, we construct a graph that captures the temporal relationship between the extracted patterns for each layer. An effective graph merging strategy finds the connection of each node to the previous layer's nodes. Finally, a graph embedding algorithm generates new representations of the created interpretable time-series features. To evaluate the performance of our proposed framework, we run extensive experiments on eight datasets of the UCR/UEA archive, along with HAR and PAM datasets. The experiments indicate the benefit of our time-aware graph-based representation in MTS classification while enriching them with more interpretability.
Knowledge graph embedding models (KGEMs) have gained considerable traction in recent years. These models learn a vector representation of knowledge graph entities and relations, a.k.a. knowledge graph embeddings (KGEs). Learning versatile KGEs is desirable as it makes them useful for a broad range of tasks. However, KGEMs are usually trained for a specific task, which makes their embeddings task-dependent. In parallel, the widespread assumption that KGEMs actually create a semantic representation of the underlying entities and relations (e.g., project similar entities closer than dissimilar ones) has been challenged. In this work, we design heuristics for generating protographs -- small, modified versions of a KG that leverage RDF/S information. The learnt protograph-based embeddings are meant to encapsulate the semantics of a KG, and can be leveraged in learning KGEs that, in turn, also better capture semantics. Extensive experiments on various evaluation benchmarks demonstrate the soundness of this approach, which we call Modular and Agnostic SCHema-based Integration of protograph Embeddings (MASCHInE). In particular, MASCHInE helps produce more versatile KGEs that yield substantially better performance for entity clustering and node classification tasks. For link prediction, using MASCHinE substantially increases the number of semantically valid predictions with equivalent rank-based performance.
This paper presents ATEM, a novel framework for studying topic evolution in scientific archives. ATEM is based on dynamic topic modeling and dynamic graph embedding techniques that explore the dynamics of content and citations of documents within a scientific corpus. ATEM explores a new notion of contextual emergence for the discovery of emerging interdisciplinary research topics based on the dynamics of citation links in topic clusters. Our experiments show that ATEM can efficiently detect emerging cross-disciplinary topics within the DBLP archive of over five million computer science articles.
Identifying and discovering drug-target interactions(DTIs) are vital steps in drug discovery and development. They play a crucial role in assisting scientists in finding new drugs and accelerating the drug development process. Recently, knowledge graph and knowledge graph embedding (KGE) models have made rapid advancements and demonstrated impressive performance in drug discovery. However, such models lack authenticity and accuracy in drug target identification, leading to an increased misjudgment rate and reduced drug development efficiency. To address these issues, we focus on the problem of drug-target interactions, with knowledge mapping as the core technology. Specifically, a causal intervention-based confidence measure is employed to assess the triplet score to improve the accuracy of the drug-target interaction prediction model. Experimental results demonstrate that the developed confidence measurement method based on causal intervention can significantly enhance the accuracy of DTI link prediction, particularly for high-precision models. The predicted results are more valuable in guiding the design and development of subsequent drug development experiments, thereby significantly improving the efficiency of drug development.