Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named GraphCSC that realizes classification based on skeleton information using fixed-order structures learned in anonymous random walks manner, and component information using different size subgraphs. Two graphs are similar if their skeletons and components are both similar, thus in our model, we integrate both of them together into embeddings as graph homogeneity characterization. We demonstrate our model on different datasets in comparison with a comprehensive list of up-to-date state-of-the-art baselines, and experiments show that our work is superior in real-world graph classification tasks.
In recent years, recommender systems play a pivotal role in helping users identify the most suitable items that satisfy personal preferences. As user-item interactions can be naturally modelled as graph-structured data, variants of graph convolutional networks (GCNs) have become a well-established building block in the latest recommenders. Due to the wide utilization of sensitive user profile data, existing recommendation paradigms are likely to expose users to the threat of privacy breach, and GCN-based recommenders are no exception. Apart from the leakage of raw user data, the fragility of current recommenders under inference attacks offers malicious attackers a backdoor to estimate users' private attributes via their behavioral footprints and the recommendation results. However, little attention has been paid to developing recommender systems that can defend such attribute inference attacks, and existing works achieve attack resistance by either sacrificing considerable recommendation accuracy or only covering specific attack models or protected information. In our paper, we propose GERAI, a novel differentially private graph convolutional network to address such limitations. Specifically, in GERAI, we bind the information perturbation mechanism in differential privacy with the recommendation capability of graph convolutional networks. Furthermore, based on local differential privacy and functional mechanism, we innovatively devise a dual-stage encryption paradigm to simultaneously enforce privacy guarantee on users' sensitive features and the model optimization process. Extensive experiments show the superiority of GERAI in terms of its resistance to attribute inference attacks and recommendation effectiveness.
Feature extraction is an efficient approach for alleviating the issue of dimensionality in high-dimensional data. As a popular self-supervised learning method, contrastive learning has recently garnered considerable attention. In this study, we proposed a unified framework based on a new perspective of contrastive learning (CL) that is suitable for both unsupervised and supervised feature extraction. The proposed framework first constructed two CL graph for uniquely defining the positive and negative pairs. Subsequently, the projection matrix was determined by minimizing the contrastive loss function. In addition, the proposed framework considered both similar and dissimilar samples to unify unsupervised and supervised feature extraction. Moreover, we propose the three specific methods: unsupervised contrastive learning method, supervised contrastive learning method 1 ,and supervised contrastive learning method 2. Finally, the numerical experiments on five real datasets demonstrated the superior performance of the proposed framework in comparison to the existing methods.
Embedding entities and relations of a knowledge graph in a low-dimensional space has shown impressive performance in predicting missing links between entities. Although progresses have been achieved, existing methods are heuristically motivated and theoretical understanding of such embeddings is comparatively underdeveloped. This paper extends the random walk model (Arora et al., 2016a) of word embeddings to Knowledge Graph Embeddings (KGEs) to derive a scoring function that evaluates the strength of a relation R between two entities h (head) and t (tail). Moreover, we show that marginal loss minimisation, a popular objective used in much prior work in KGE, follows naturally from the log-likelihood ratio maximisation under the probabilities estimated from the KGEs according to our theoretical relationship. We propose a learning objective motivated by the theoretical analysis to learn KGEs from a given knowledge graph. Using the derived objective, accurate KGEs are learnt from FB15K237 and WN18RR benchmark datasets, providing empirical evidence in support of the theory.
We propose a new framework for computing the embeddings of large-scale graphs on a single machine. A graph embedding is a fixed length vector representation for each node (and/or edge-type) in a graph and has emerged as the de-facto approach to apply modern machine learning on graphs. We identify that current systems for learning the embeddings of large-scale graphs are bottlenecked by data movement, which results in poor resource utilization and inefficient training. These limitations require state-of-the-art systems to distribute training across multiple machines. We propose Marius, a system for efficient training of graph embeddings that leverages partition caching and buffer-aware data orderings to minimize disk access and interleaves data movement with computation to maximize utilization. We compare Marius against two state-of-the-art industrial systems on a diverse array of benchmarks. We demonstrate that Marius achieves the same level of accuracy but is up to one order of magnitude faster. We also show that Marius can scale training to datasets an order of magnitude beyond a single machine's GPU and CPU memory capacity, enabling training of configurations with more than a billion edges and 550 GB of total parameters on a single machine with 16 GB of GPU memory and 64 GB of CPU memory. Marius is open-sourced at www.marius-project.org.
Objective: Multi-modal functional magnetic resonance imaging (fMRI) can be used to make predictions about individual behavioral and cognitive traits based on brain connectivity networks. Methods: To take advantage of complementary information from multi-modal fMRI, we propose an interpretable multi-modal graph convolutional network (MGCN) model, incorporating the fMRI time series and the functional connectivity (FC) between each pair of brain regions. Specifically, our model learns a graph embedding from individual brain networks derived from multi-modal data. A manifold-based regularization term is then enforced to consider the relationships of subjects both within and between modalities. Furthermore, we propose the gradient-weighted regression activation mapping (Grad-RAM) and the edge mask learning to interpret the model, which is used to identify significant cognition-related biomarkers. Results: We validate our MGCN model on the Philadelphia Neurodevelopmental Cohort to predict individual wide range achievement test (WRAT) score. Our model obtains superior predictive performance over GCN with a single modality and other competing approaches. The identified biomarkers are cross-validated from different approaches. Conclusion and Significance: This paper develops a new interpretable graph deep learning framework for cognitive ability prediction, with the potential to overcome the limitations of several current data-fusion models. The results demonstrate the power of MGCN in analyzing multi-modal fMRI and discovering significant biomarkers for human brain studies.
With the rapid development of biomedical software and hardware, a large amount of relational data interlinking genes, proteins, chemical components, drugs, diseases, and symptoms has been collected for modern biomedical research. Many graph-based learning methods have been proposed to analyze such type of data, giving a deeper insight into the topology and knowledge behind the biomedical data, which greatly benefit to both academic research and industrial application for human healthcare. However, the main difficulty is how to handle high dimensionality and sparsity of the biomedical graphs. Recently, graph embedding methods provide an effective and efficient way to address the above issues. It converts graph-based data into a low dimensional vector space where the graph structural properties and knowledge information are well preserved. In this survey, we conduct a literature review of recent developments and trends in applying graph embedding methods for biomedical data. We also introduce important applications and tasks in the biomedical domain as well as associated public biomedical datasets.
In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown concepts, these representations typically assume that all concepts are known a priori, and incorporating new information requires all concepts to be learned afresh. Our work relaxes this limiting assumption of existing representations and tackles the incremental knowledge graph embedding problem by leveraging the principles of a range of continual learning methods. Through an experimental evaluation with several knowledge graphs and embedding representations, we provide insights about trade-offs for practitioners to match a semantics-driven robotics applications to a suitable continual knowledge graph embedding method.
This paper proposes a discrete knowledge graph (KG) embedding (DKGE) method, which projects KG entities and relations into the Hamming space based on a computationally tractable discrete optimization algorithm, to solve the formidable storage and computation cost challenges in traditional continuous graph embedding methods. The convergence of DKGE can be guaranteed theoretically. Extensive experiments demonstrate that DKGE achieves superior accuracy than classical hashing functions that map the effective continuous embeddings into discrete codes. Besides, DKGE reaches comparable accuracy with much lower computational complexity and storage compared to many continuous graph embedding methods.
In this work, we propose a novel Knowledge Graph Embedding (KGE) strategy, called M\"{o}biusE, in which the entities and relations are embedded to the surface of a M\"{o}bius ring. The proposition of such a strategy is inspired by the classic TorusE, in which the addition of two arbitrary elements is subject to a modulus operation. In this sense, TorusE naturally guarantees the critical boundedness of embedding vectors in KGE. However, the nonlinear property of addition operation on Torus ring is uniquely derived by the modulus operation, which in some extent restricts the expressiveness of TorusE. As a further generalization of TorusE, M\"{o}biusE also uses modulus operation to preserve the closeness of addition operation on it, but the coordinates on M\"{o}bius ring interacts with each other in the following way: {\em \color{red} any vector on the surface of a M\"{o}bius ring moves along its parametric trace will goes to the right opposite direction after a cycle}. Hence, M\"{o}biusE assumes much more nonlinear representativeness than that of TorusE, and in turn it generates much more precise embedding results. In our experiments, M\"{o}biusE outperforms TorusE and other classic embedding strategies in several key indicators.
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks present dynamic behavior, including topological evolution, feature evolution, and diffusion. Therefore, several methods for embedding dynamic graphs have been proposed to learn network representations over time, facing novel challenges, such as time-domain modeling, temporal features to be captured, and the temporal granularity to be embedded. In this survey, we overview dynamic graph embedding, discussing its fundamentals and the recent advances developed so far. We introduce the formal definition of dynamic graph embedding, focusing on the problem setting and introducing a novel taxonomy for dynamic graph embedding input and output. We further explore different dynamic behaviors that may be encompassed by embeddings, classifying by topological evolution, feature evolution, and processes on networks. Afterward, we describe existing techniques and propose a taxonomy for dynamic graph embedding techniques based on algorithmic approaches, from matrix and tensor factorization to deep learning, random walks, and temporal point processes. We also elucidate main applications, including dynamic link prediction, anomaly detection, and diffusion prediction, and we further state some promising research directions in the area.
Event detection has been an important task in transportation, whose task is to detect points in time when large events disrupts a large portion of the urban traffic network. Travel information {Origin-Destination} (OD) matrix data by map service vendors has large potential to give us insights to discover historic patterns and distinguish anomalies. However, to fully capture the spatial and temporal traffic patterns remains a challenge, yet serves a crucial role for effective anomaly detection. Meanwhile, existing anomaly detection methods have not well-addressed the extreme data sparsity and high-dimension challenges, which are common in OD matrix datasets. To tackle these challenges, we formulate the problem in a novel way, as detecting anomalies in a set of directed weighted graphs representing the traffic conditions at each time interval. We further propose \textit{Context augmented Graph Autoencoder} (\textbf{Con-GAE }), that leverages graph embedding and context embedding techniques to capture the spatial traffic network patterns while working around the data sparsity and high-dimensionality issue. Con-GAE adopts an autoencoder framework and detect anomalies via semi-supervised learning. Extensive experiments show that our method can achieve up can achieve a 0.1-0.4 improvements of the area under the curve (AUC) score over state-of-art anomaly detection baselines, when applied on several real-world large scale OD matrix datasets.
It is common practice of the outlier mining community to repurpose classification datasets toward evaluating various detection models. To that end, often a binary classification dataset is used, where samples from one of the classes is designated as the inlier samples, and the other class is substantially down-sampled to create the ground-truth outlier samples. Graph-level outlier detection (GLOD) is rarely studied but has many potentially influential real-world applications. In this study, we identify an intriguing issue with repurposing graph classification datasets for GLOD. We find that ROC-AUC performance of the models changes significantly (flips from high to very low, even worse than random) depending on which class is down-sampled. Interestingly, ROC-AUCs on these two variants approximately sum to 1 and their performance gap is amplified with increasing propagations for a certain family of propagation based outlier detection models. We carefully study the graph embedding space produced by propagation based models and find two driving factors: (1) disparity between within-class densities which is amplified by propagation, and (2)overlapping support (mixing of embeddings) across classes. We also study other graph embedding methods and downstream outlier detectors, and find that the intriguing performance flip issue still widely exists but which version of the downsample achieves higher performance may vary. Thoughtful analysis over comprehensive results further deeper our understanding of the established issue.
Graph Neural Networks (GNNs) are widely used in graph representation learning. However, most GNN methods are designed for either homogeneous or heterogeneous graphs. In this paper, we propose a new model, Hop-Hop Relation-aware Graph Neural Network (HHR-GNN), to unify representation learning for these two types of graphs. HHR-GNN learns a personalized receptive field for each node by leveraging knowledge graph embedding to learn relation scores between the central node's representations at different hops. In neighborhood aggregation, our model simultaneously allows for hop-aware projection and aggregation. This mechanism enables the central node to learn a hop-wise neighborhood mixing that can be applied to both homogeneous and heterogeneous graphs. Experimental results on five benchmarks show the competitive performance of our model compared to state-of-the-art GNNs, e.g., up to 13K faster in terms of time cost per training epoch on large heterogeneous graphs.
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and heterogeneous characteristics of industrial size networks. Graph embedding techniques can be effective in converting high-dimensional sparse graphs into low-dimensional, dense and continuous vector spaces, preserving maximally the graph structure properties. Another type of emerging graph embedding employs Gaussian distribution-based graph embedding with important uncertainty estimation. The main goal of graph embedding methods is to pack every node's properties into a vector with a smaller dimension, hence, node similarity in the original complex irregular spaces can be easily quantified in the embedded vector spaces using standard metrics. The generated nonlinear and highly informative graph embeddings in the latent space can be conveniently used to address different downstream graph analytics tasks (e.g., node classification, link prediction, community detection, visualization, etc.). In this Review, we present some fundamental concepts in graph analytics and graph embedding methods, focusing in particular on random walk-based and neural network-based methods. We also discuss the emerging deep learning-based dynamic graph embedding methods. We highlight the distinct advantages of graph embedding methods in four diverse applications, and present implementation details and references to open-source software as well as available databases in the Appendix for the interested readers to start their exploration into graph analytics.
Bipartite graph embedding has recently attracted much attention due to the fact that bipartite graphs are widely used in various application domains. Most previous methods, which adopt random walk-based or reconstruction-based objectives, are typically effective to learn local graph structures. However, the global properties of bipartite graph, including community structures of homogeneous nodes and long-range dependencies of heterogeneous nodes, are not well preserved. In this paper, we propose a bipartite graph embedding called BiGI to capture such global properties by introducing a novel local-global infomax objective. Specifically, BiGI first generates a global representation which is composed of two prototype representations. BiGI then encodes sampled edges as local representations via the proposed subgraph-level attention mechanism. Through maximizing the mutual information between local and global representations, BiGI enables nodes in bipartite graph to be globally relevant. Our model is evaluated on various benchmark datasets for the tasks of top-K recommendation and link prediction. Extensive experiments demonstrate that BiGI achieves consistent and significant improvements over state-of-the-art baselines. Detailed analyses verify the high effectiveness of modeling the global properties of bipartite graph.
This paper introduces a graphical representation approach of prosody boundary (GraphPB) in the task of Chinese speech synthesis, intending to parse the semantic and syntactic relationship of input sequences in a graphical domain for improving the prosody performance. The nodes of the graph embedding are formed by prosodic words, and the edges are formed by the other prosodic boundaries, namely prosodic phrase boundary (PPH) and intonation phrase boundary (IPH). Different Graph Neural Networks (GNN) like Gated Graph Neural Network (GGNN) and Graph Long Short-term Memory (G-LSTM) are utilised as graph encoders to exploit the graphical prosody boundary information. Graph-to-sequence model is proposed and formed by a graph encoder and an attentional decoder. Two techniques are proposed to embed sequential information into the graph-to-sequence text-to-speech model. The experimental results show that this proposed approach can encode the phonetic and prosody rhythm of an utterance. The mean opinion score (MOS) of these GNN models shows comparative results with the state-of-the-art sequence-to-sequence models with better performance in the aspect of prosody. This provides an alternative approach for prosody modelling in end-to-end speech synthesis.
Knowledge graph (KG), integrating complex information and containing rich semantics, is widely considered as side information to enhance the recommendation systems. However, most of the existing KG-based methods concentrate on encoding the structural information in the graph, without utilizing the collaborative signals in user-item interaction data, which are important for understanding user preferences. Therefore, the representations learned by these models are insufficient for representing semantic information of users and items in the recommendation environment. The combination of both kinds of data provides a good chance to solve this problem. To tackle this research gap, we propose a novel duet representation learning framework named \sysname to fuse local information (user-item interaction data) and global information (external knowledge graph) for the top-$N$ recommendation, which is composed of two separate sub-models. One learns the local representations by discovering the inner correlations in local information with a knowledge-aware co-attention mechanism, and another learns the global representations by encoding the knowledge associations in global information with a relation-aware attention network. The two sub-models are jointly trained as part of the semantic fusion network to compute the user preferences, which discriminates the contribution of the two sub-models under the special context. We conduct experiments on two real-world datasets, and the evaluations show that KADM significantly outperforms state-of-art methods. Further ablation studies confirm that the duet architecture performs significantly better than either sub-model on the recommendation tasks.
It has been well established that Functional Connectomes (FCs), as estimated from functional MRI (fMRI) data, have an individual fingerprint that can be used to identify an individual from a population (subject-identification). Although identification rate is high when using resting-state FCs, other tasks show moderate to low values. Furthermore, identification rate is task-dependent, and is low when distinct cognitive states, as captured by different fMRI tasks, are compared. Here we propose an embedding framework, GEFF (Graph Embedding for Functional Fingerprinting), based on group-level decomposition of FCs into eigenvectors. GEFF creates an eigenspace representation of a group of subjects using one or more task FCs (Learning Stage). In the Identification Stage, we compare new instances of FCs from the Learning subjects within this eigenspace (validation dataset). The validation dataset contains FCs either from the same tasks as the Learning dataset or from the remaining tasks that were not included in Learning. Assessment of validation FCs within the eigenspace results in significantly increased subject-identification rates for all fMRI tasks tested and potentially task-independent fingerprinting process. It is noteworthy that combining resting-state with one fMRI task for GEFF Learning Stage covers most of the cognitive space for subject identification. In addition to subject-identification, GEFF was also used for identification of cognitive states, i.e. to identify the task associated to a given FC, regardless of the subject being already in the Learning dataset or not (subject-independent task-identification). In addition, we also show that eigenvectors from the Learning Stage can be characterized as task-dominant, subject dominant or neither, providing a deeper insight into the extent of variance in functional connectivity across individuals and cognitive states.
Collaborative Knowledge Bases such as Freebase and Wikidata mention multiple professions and nationalities for a particular entity. The goal of the WSDM Cup 2017 Triplet Scoring Challenge was to calculate relevance scores between an entity and its professions/nationalities. Such scores are a fundamental ingredient when ranking results in entity search. This paper proposes a novel approach to ensemble an advanced Knowledge Graph Embedding Model with a simple bag-of-words model. The former deals with hidden pragmatics and deep semantics whereas the latter handles text-based retrieval and low-level semantics.