-Background. Network neuroscience examines the brain as a complex system represented by a network (or connectome), providing deeper insights into the brain morphology and function, allowing the identification of atypical brain connectivity alterations, which can be used as diagnostic markers of neurological disorders. -Existing Methods. Graph embedding methods which map data samples (e.g., brain networks) into a low dimensional space have been widely used to explore the relationship between samples for classification or prediction tasks. However, the majority of these works are based on modeling the pair-wise relationships between samples, failing to capture their higher-order relationships. -New Method. In this paper, inspired by the nascent field of geometric deep learning, we propose Hypergraph U-Net (HUNet), a novel data embedding framework leveraging the hypergraph structure to learn low-dimensional embeddings of data samples while capturing their high-order relationships. Specifically, we generalize the U-Net architecture, naturally operating on graphs, to hypergraphs by improving local feature aggregation and preserving the high-order relationships present in the data. -Results. We tested our method on small-scale and large-scale heterogeneous brain connectomic datasets including morphological and functional brain networks of autistic and demented patients, respectively. -Conclusion. Our HUNet outperformed state-of-the-art geometric graph and hypergraph data embedding techniques with a gain of 4-14% in classification accuracy, demonstrating both scalability and generalizability. HUNet code is available at https://github.com/basiralab/HUNet.
Name disambiguation aims to identify unique authors with the same name. Existing name disambiguation methods always exploit author attributes to enhance disambiguation results. However, some discriminative author attributes (e.g., email and affiliation) may change because of graduation or job-hopping, which will result in the separation of the same author's papers in digital libraries. Although these attributes may change, an author's co-authors and research topics do not change frequently with time, which means that papers within a period have similar text and relation information in the academic network. Inspired by this idea, we introduce Multi-view Attention-based Pairwise Recurrent Neural Network (MA-PairRNN) to solve the name disambiguation problem. We divided papers into small blocks based on discriminative author attributes and blocks of the same author will be merged according to pairwise classification results of MA-PairRNN. MA-PairRNN combines heterogeneous graph embedding learning and pairwise similarity learning into a framework. In addition to attribute and structure information, MA-PairRNN also exploits semantic information by meta-path and generates node representation in an inductive way, which is scalable to large graphs. Furthermore, a semantic-level attention mechanism is adopted to fuse multiple meta-path based representations. A Pseudo-Siamese network consisting of two RNNs takes two paper sequences in publication time order as input and outputs their similarity. Results on two real-world datasets demonstrate that our framework has a significant and consistent improvement of performance on the name disambiguation task. It was also demonstrated that MA-PairRNN can perform well with a small amount of training data and have better generalization ability across different research areas.
Recently, the surge in popularity of Internet of Things (IoT), mobile devices, social media, etc. has opened up a large source for graph data. Graph embedding has been proved extremely useful to learn low-dimensional feature representations from graph structured data. These feature representations can be used for a variety of prediction tasks from node classification to link prediction. However, existing graph embedding methods do not consider users' privacy to prevent inference attacks. That is, adversaries can infer users' sensitive information by analyzing node representations learned from graph embedding algorithms. In this paper, we propose Adversarial Privacy Graph Embedding (APGE), a graph adversarial training framework that integrates the disentangling and purging mechanisms to remove users' private information from learned node representations. The proposed method preserves the structural information and utility attributes of a graph while concealing users' private attributes from inference attacks. Extensive experiments on real-world graph datasets demonstrate the superior performance of APGE compared to the state-of-the-arts. Our source code can be found at https://github.com/uJ62JHD/Privacy-Preserving-Social-Network-Embedding.
Graphs have been widely used to represent complex data in many applications. Efficient and effective analysis of graphs is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses ML to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding (GE) methods and end-to-end (E2E) learning methods. For GE methods, learning graph embedding has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For E2E learning methods, the learning of graph embeddings does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.
Multivariate time series forecasting, which analyzes historical time series to predict future trends, can effectively help decision-making. Complex relations among variables in MTS, including static, dynamic, predictable, and latent relations, have made it possible to mining more features of MTS. Modeling complex relations are not only essential in characterizing latent dependency as well as modeling temporal dependence but also brings great challenges in the MTS forecasting task. However, existing methods mainly focus on modeling certain relations among MTS variables. In this paper, we propose a novel end-to-end deep learning model, termed Multivariate Time Series Forecasting via Heterogeneous Graph Neural Networks (MTHetGNN). To characterize complex relations among variables, a relation embedding module is designed in MTHetGNN, where each variable is regarded as a graph node, and each type of edge represents a specific static or dynamic relationship. Meanwhile, a temporal embedding module is introduced for time series features extraction, where involving convolutional neural network (CNN) filters with different perception scales. Finally, a heterogeneous graph embedding module is adopted to handle the complex structural information generated by the two modules. Three benchmark datasets from the real world are used to evaluate the proposed MTHetGNN. The comprehensive experiments show that MTHetGNN achieves state-of-the-art results in the MTS forecasting task.
Link prediction is the task of predicting missing connections between entities in the knowledge graph (KG). While various forms of models are proposed for the link prediction task, most of them are designed based on a few known relation patterns in several well-known datasets. Due to the diversity and complexity nature of the real-world KGs, it is inherently difficult to design a model that fits all datasets well. To address this issue, previous work has tried to use Automated Machine Learning (AutoML) to search for the best model for a given dataset. However, their search space is limited only to bilinear model families. In this paper, we propose a novel Neural Architecture Search (NAS) framework for the link prediction task. First, the embeddings of the input triplet are refined by the Representation Search Module. Then, the prediction score is searched within the Score Function Search Module. This framework entails a more general search space, which enables us to take advantage of several mainstream model families, and thus it can potentially achieve better performance. We relax the search space to be continuous so that the architecture can be optimized efficiently using gradient-based search strategies. Experimental results on several benchmark datasets demonstrate the effectiveness of our method compared with several state-of-the-art approaches.
Commonsense knowledge graph reasoning(CKGR) is the task of predicting a missing entity given one existing and the relation in a commonsense knowledge graph (CKG). Existing methods can be classified into two categories generation method and selection method. Each method has its own advantage. We theoretically and empirically compare the two methods, finding the selection method is more suitable than the generation method in CKGR. Given the observation, we further combine the structure of neural Text Encoder and Knowledge Graph Embedding models to solve the selection method's two problems, achieving competitive results. We provide a basic framework and baseline model for subsequent CKGR tasks by selection methods.
Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: \url{https://github.com/daiquocnguyen/QGNN}.
Capturing the composition patterns of relations is a vital task in knowledge graph completion. It also serves as a fundamental step towards multi-hop reasoning over learned knowledge. Previously, several rotation-based translational methods have been developed to model composite relations using the product of a series of complex-valued diagonal matrices. However, these methods tend to make several oversimplified assumptions on the composite relations, e.g., forcing them to be commutative, independent from entities and lacking semantic hierarchy. To systematically tackle these problems, we have developed a novel knowledge graph embedding method, named DensE, to provide an improved modeling scheme for the complex composition patterns of relations. In particular, our method decomposes each relation into an SO(3) group-based rotation operator and a scaling operator in the three dimensional (3-D) Euclidean space. This design principle leads to several advantages of our method: (1) For composite relations, the corresponding diagonal relation matrices can be non-commutative, reflecting a predominant scenario in real world applications; (2) Our model preserves the natural interaction between relational operations and entity embeddings; (3) The scaling operation provides the modeling power for the intrinsic semantic hierarchical structure of entities; (4) The enhanced expressiveness of DensE is achieved with high computational efficiency in terms of both parameter size and training time; and (5) Modeling entities in Euclidean space instead of quaternion space keeps the direct geometrical interpretations of relational patterns. Experimental results on multiple benchmark knowledge graphs show that DensE outperforms the current state-of-the-art models for missing link prediction, especially on composite relations.
Node representation learning for directed graphs is critically important to facilitate many graph mining tasks. To capture the directed edges between nodes, existing methods mostly learn two embedding vectors for each node, source vector and target vector. However, these methods learn the source and target vectors separately. For the node with very low indegree or outdegree, the corresponding target vector or source vector cannot be effectively learned. In this paper, we propose a novel Directed Graph embedding framework based on Generative Adversarial Network, called DGGAN. The main idea is to use adversarial mechanisms to deploy a discriminator and two generators that jointly learn each node's source and target vectors. For a given node, the two generators are trained to generate its fake target and source neighbor nodes from the same underlying distribution, and the discriminator aims to distinguish whether a neighbor node is real or fake. The two generators are formulated into a unified framework and could mutually reinforce each other to learn more robust source and target vectors. Extensive experiments show that DGGAN consistently and significantly outperforms existing state-of-the-art methods across multiple graph mining tasks on directed graphs.
Information technology has spread widely, and extraordinarily large amounts of data have been made accessible to users, which has made it challenging to select data that are in accordance with user needs. For the resolution of the above issue, recommender systems have emerged, which much help users go through the process of decision-making and selecting relevant data. A recommender system predicts users behavior to be capable of detecting their interests and needs, and it often uses the classification technique for this purpose. It may not be sufficiently accurate to employ individual classification, where not all cases can be examined, which makes the method inappropriate to specific problems. In this research, group classification and the ensemble learning technique were used for increasing prediction accuracy in recommender systems. Another issue that is raised here concerns user analysis. Given the large size of the data and a large number of users, the process of user needs analysis and prediction (using a graph in most cases, representing the relations between users and their selected items) is complicated and cumbersome in recommender systems. Graph embedding was also proposed for resolution of this issue, where all or part of user behavior can be simulated through the generation of several vectors, resolving the problem of user behavior analysis to a large extent while maintaining high efficiency. In this research, individuals most similar to the target user were classified using ensemble learning, fuzzy rules, and the decision tree, and relevant recommendations were then made to each user with a heterogeneous knowledge graph and embedding vectors. This study was performed on the MovieLens datasets, and the obtained results indicated the high efficiency of the presented method.
Recently, knowledge graph embeddings (KGEs) received significant attention, and several software libraries have been developed for training and evaluating KGEs. While each of them addresses specific needs, we re-designed and re-implemented PyKEEN, one of the first KGE libraries, in a community effort. PyKEEN 1.0 enables users to compose knowledge graph embedding models (KGEMs) based on a wide range of interaction models, training approaches, loss functions, and permits the explicit modeling of inverse relations. Besides, an automatic memory optimization has been realized in order to exploit the provided hardware optimally, and through the integration of Optuna extensive hyper-parameter optimization (HPO) functionalities are provided.
Program similarity is a fundamental concept, central to the solution of software engineering tasks such as software plagiarism, clone identification, code refactoring and code search. Accurate similarity estimation between programs requires an in-depth understanding of their structure, semantics and flow. A control flow graph (CFG), is a graphical representation of a program which captures its logical control flow and hence its semantics. A common approach is to estimate program similarity by analysing CFGs using graph similarity measures, e.g. graph edit distance (GED). However, graph edit distance is an NP-hard problem and computationally expensive, making the application of graph similarity techniques to complex software programs impractical. This study intends to examine the effectiveness of graph neural networks to estimate program similarity, by analysing the associated control flow graphs. We introduce funcGNN, which is a graph neural network trained on labeled CFG pairs to predict the GED between unseen program pairs by utilizing an effective embedding vector. To our knowledge, this is the first time graph neural networks have been applied on labeled CFGs for estimating the similarity between high-level language programs. Results: We demonstrate the effectiveness of funcGNN to estimate the GED between programs and our experimental analysis demonstrates how it achieves a lower error rate (0.00194), with faster (23 times faster than the quickest traditional GED approximation method) and better scalability compared with the state of the art methods. funcGNN posses the inductive learning ability to infer program structure and generalise to unseen programs. The graph embedding of a program proposed by our methodology could be applied to several related software engineering problems (such as code plagiarism and clone identification) thus opening multiple research directions.
Knowledge graph embedding, which aims to learn the low-dimensional representations of entities and relationships, has attracted considerable research efforts recently. However, most knowledge graph embedding methods focus on the structural relationships in fixed triples while ignoring the temporal information. Currently, existing time-aware graph embedding methods only focus on the factual plausibility, while ignoring the temporal smoothness which models the interactions between a fact and its contexts, and thus can capture fine-granularity temporal relationships. This leads to the limited performance of embedding related applications. To solve this problem, this paper presents a Robustly Time-aware Graph Embedding (RTGE) method by incorporating temporal smoothness. Two major innovations of our paper are presented here. At first, RTGE integrates a measure of temporal smoothness in the learning process of the time-aware graph embedding. Via the proposed additional smoothing factor, RTGE can preserve both structural information and evolutionary patterns of a given graph. Secondly, RTGE provides a general task-oriented negative sampling strategy associated with temporally-aware information, which further improves the adaptive ability of the proposed algorithm and plays an essential role in obtaining superior performance in various tasks. Extensive experiments conducted on multiple benchmark tasks show that RTGE can increase performance in entity/relationship/temporal scoping prediction tasks.
Network (or graph) embedding is the task to map the nodes of a graph to a lower dimensional vector space, such that it preserves the graph properties and facilitates the downstream network mining tasks. Real world networks often come with (community) outlier nodes, which behave differently from the regular nodes of the community. These outlier nodes can affect the embedding of the regular nodes, if not handled carefully. In this paper, we propose a novel unsupervised graph embedding approach (called DMGD) which integrates outlier and community detection with node embedding. We extend the idea of deep support vector data description to the framework of graph embedding when there are multiple communities present in the given network, and an outlier is characterized relative to its community. We also show the theoretical bounds on the number of outliers detected by DMGD. Our formulation boils down to an interesting minimax game between the outliers, community assignments and the node embedding function. We also propose an efficient algorithm to solve this optimization framework. Experimental results on both synthetic and real world networks show the merit of our approach compared to state-of-the-arts.
In recent years, substantial progress has been made on Graph Convolutional Networks (GCNs). However, the computing of GCN usually requires a large memory space for keeping the entire graph. In consequence, GCN is not flexible enough, especially for large scale graphs in complex real-world applications. Fortunately, methods based on Matrix Factorization (MF) naturally support constructing mini-batches, and thus are more friendly to distributed computing compared with GCN. Accordingly, in this paper, we analyze the connections between GCN and MF, and simplify GCN as matrix factorization with unitization and co-training. Furthermore, under the guidance of our analysis, we propose an alternative model to GCN named Unitized and Co-training Matrix Factorization (UCMF). Extensive experiments have been conducted on several real-world datasets. On the task of semi-supervised node classification, the experimental results illustrate that UCMF achieves similar or superior performances compared with GCN. Meanwhile, distributed UCMF significantly outperforms distributed GCN methods, which shows that UCMF can greatly benefit large scale and complex real-world applications. Moreover, we have also conducted experiments on a typical task of graph embedding, i.e., community detection, and the proposed UCMF model outperforms several representative graph embedding models.
Knowledge graphs (KGs) composed of users, objects, and tags are widely used in web applications ranging from E-commerce, social media sites to news portals. This paper concentrates on an attractive application which aims to predict the object-tag links in the KG for better tag recommendation and object explanation. When predicting the object-tag links, both the first-order and high-order proximities between entities in the KG propagate essential similarity information for better prediction. Most existing methods focus on preserving the first-order proximity between entities in the KG. However, they cannot capture the high-order proximities in an explicit way, and the adopted margin-based criterion cannot measure the first-order proximity on the global structure accurately. In this paper, we propose a novel approach named Dual Graph Embedding (DGE) that models both the first-order and high-order proximities in the KG via an auto-encoding architecture to facilitate better object-tag relation inference. Here the dual graphs contain an object graph and a tag graph that explicitly depict the high-order object-object and tag-tag proximities in the KG. The dual graph encoder in DGE then encodes these high-order proximities in the dual graphs into entity embeddings. The decoder formulates a skip-gram objective that maximizes the first-order proximity between observed object-tag pairs over the global proximity structure. With the supervision of the decoder, the embeddings derived by the encoder will be refined to capture both the first-order and high-order proximities in the KG for better link prediction. Extensive experiments on three real-world datasets demonstrate that DGE outperforms the state-of-the-art methods.
Neural Architecture Search (NAS) automates and prospers the design of neural networks. Estimator-based NAS has been proposed recently to model the relationship between architectures and their performance to enable scalable and flexible search. However, existing estimator-based methods encode the architecture into a latent space without considering graph similarity. Ignoring graph similarity in node-based search space may induce a large inconsistency between similar graphs and their distance in the continuous encoding space, leading to inaccurate encoding representation and/or reduced representation capacity that can yield sub-optimal search results. To preserve graph correlation information in encoding, we propose NASGEM which stands for Neural Architecture Search via Graph Embedding Method. NASGEM is driven by a novel graph embedding method equipped with similarity measures to capture the graph topology information. By precisely estimating the graph distance and using an auxiliary Weisfeiler-Lehman kernel to guide the encoding, NASGEM can utilize additional structural information to get more accurate graph representation to improve the search efficiency. GEMNet, a set of networks discovered by NASGEM, consistently outperforms networks crafted by existing search methods in classification tasks, i.e., with 0.4%-3.6% higher accuracy while having 11%- 21% fewer Multiply-Accumulates. We further transfer GEMNet for COCO object detection. In both one-stage and twostage detectors, our GEMNet surpasses its manually-crafted and automatically-searched counterparts.
Interpretation of different writing styles, unconstrained cursiveness and relationship between different primitive parts is an essential and challenging task for recognition of handwritten characters. As feature representation is inadequate, appropriate interpretation/description of handwritten characters seems to be a challenging task. Although existing research in handwritten characters is extensive, it still remains a challenge to get the effective representation of characters in feature space. In this paper, we make an attempt to circumvent these problems by proposing an approach that exploits the robust graph representation and spectral graph embedding concept to characterise and effectively represent handwritten characters, taking into account writing styles, cursiveness and relationships. For corroboration of the efficacy of the proposed method, extensive experiments were carried out on the standard handwritten numeral Computer Vision Pattern Recognition, Unit of Indian Statistical Institute Kolkata dataset. The experimental results demonstrate promising findings, which can be used in future studies.
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best configuration of product space is a resource-intensive procedure, which reduces the practical applicability of the idea. We generalize the concept of product space and introduce an overlapping space that does not have the configuration search problem. The main idea is to allow subsets of coordinates to be shared between spaces of different types (Euclidean, hyperbolic, spherical). As a result, parameter optimization automatically learns the optimal configuration. Additionally, overlapping spaces allow for more compact representations since their geometry is more complex. Our experiments confirm that overlapping spaces outperform the competitors in graph embedding tasks. Here, we consider both distortion setup, where the aim is to preserve distances, and ranking setup, where the relative order should be preserved. The proposed method effectively solves the problem and outperforms the competitors in both settings. We also perform an empirical analysis in a realistic information retrieval task, where we compare all spaces by incorporating them into DSSM. In this case, the proposed overlapping space consistently achieves nearly optimal results without any configuration tuning. This allows for reducing training time, which can be significant in large-scale applications.