Learning and reasoning over graphs is increasingly done by means of probabilistic models, e.g. exponential random graph models, graph embedding models, and graph neural networks. When graphs are modeling relations between people, however, they will inevitably reflect biases, prejudices, and other forms of inequity and inequality. An important challenge is thus to design accurate graph modeling approaches while guaranteeing fairness according to the specific notion of fairness that the problem requires. Yet, past work on the topic remains scarce, is limited to debiasing specific graph modeling methods, and often aims to ensure fairness in an indirect manner. We propose a generic approach applicable to most probabilistic graph modeling approaches. Specifically, we first define the class of fair graph models corresponding to a chosen set of fairness criteria. Given this, we propose a fairness regularizer defined as the KL-divergence between the graph model and its I-projection onto the set of fair models. We demonstrate that using this fairness regularizer in combination with existing graph modeling approaches efficiently trades-off fairness with accuracy, whereas the state-of-the-art models can only make this trade-off for the fairness criterion that they were specifically designed for.
Dynamic graphs arise in a plethora of practical scenarios such as social networks, communication networks, and financial transaction networks. Given a dynamic graph, it is fundamental and essential to learn a graph representation that is expected not only to preserve structural proximity but also jointly capture the time-evolving patterns. Recently, graph convolutional network (GCN) has been widely explored and used in non-Euclidean application domains. The main success of GCN, especially in handling dependencies and passing messages within nodes, lies in its approximation to Laplacian smoothing. As a matter of fact, this smoothing technique can not only encourage must-link node pairs to get closer but also push cannot-link pairs to shrink together, which potentially cause serious feature shrink or oversmoothing problem, especially when stacking graph convolution in multiple layers or steps. For learning time-evolving patterns, a natural solution is to preserve historical state and combine it with the current interactions to obtain the most recent representation. Then the serious feature shrink or oversmoothing problem could happen when stacking graph convolution explicitly or implicitly according to current prevalent methods, which would make nodes too similar to distinguish each other. To solve this problem in dynamic graph embedding, we analyze the shrinking properties in the node embedding space at first, and then design a simple yet versatile method, which exploits L2 feature normalization constraint to rescale all nodes to hypersphere of a unit ball so that nodes would not shrink together, and yet similar nodes can still get closer. Extensive experiments on four real-world dynamic graph datasets compared with competitive baseline models demonstrate the effectiveness of the proposed method.
Graph neural networks (GNNs) have attracted tremendous attention from the graph learning community in recent years. It has been widely adopted in various real-world applications from diverse domains, such as social networks and biological graphs. The research and applications of graph deep learning present new challenges, including the sparse nature of graph data, complicated training of GNNs, and non-standard evaluation of graph tasks. To tackle the issues, we present CogDL, a comprehensive library for graph deep learning that allows researchers and practitioners to conduct experiments, compare methods, and build applications with ease and efficiency. In CogDL, we propose a unified design for the training and evaluation of GNN models for various graph tasks, making it unique among existing graph learning libraries. By utilizing this unified trainer, CogDL can optimize the GNN training loop with several training techniques, such as mixed precision training. Moreover, we develop efficient sparse operators for CogDL, enabling it to become the most competitive graph library for efficiency. Another important CogDL feature is its focus on ease of use with the aim of facilitating open and reproducible research of graph learning. We leverage CogDL to report and maintain benchmark results on fundamental graph tasks, which can be reproduced and directly used by the community.
While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.
Semi-supervised learning (SSL) has tremendous value in practice due to its ability to utilize both labeled data and unlabelled data. An important class of SSL methods is to naturally represent data as graphs such that the label information of unlabelled samples can be inferred from the graphs, which corresponds to graph-based semi-supervised learning (GSSL) methods. GSSL methods have demonstrated their advantages in various domains due to their uniqueness of structure, the universality of applications, and their scalability to large scale data. Focusing on this class of methods, this work aims to provide both researchers and practitioners with a solid and systematic understanding of relevant advances as well as the underlying connections among them. This makes our paper distinct from recent surveys that cover an overall picture of SSL methods while neglecting fundamental understanding of GSSL methods. In particular, a major contribution of this paper lies in a new generalized taxonomy for GSSL, including graph regularization and graph embedding methods, with the most up-to-date references and useful resources such as codes, datasets, and applications. Furthermore, we present several potential research directions as future work with insights into this rapidly growing field.
Deep learning is effective in graph analysis. It is widely applied in many related areas, such as link prediction, node classification, community detection, and graph classification etc. Graph embedding, which learns low-dimensional representations for vertices or edges in the graph, usually employs deep models to derive the embedding vector. However, these models are vulnerable. We envision that graph embedding methods based on deep models can be easily attacked using adversarial examples. Thus, in this paper, we propose Graphfool, a novel targeted label adversarial attack on graph embedding. It can generate adversarial graph to attack graph embedding methods via classifying boundary and gradient information in graph convolutional network (GCN). Specifically, we perform the following steps: 1),We first estimate the classification boundaries of different classes. 2), We calculate the minimal perturbation matrix to misclassify the attacked vertex according to the target classification boundary. 3), We modify the adjacency matrix according to the maximal absolute value of the disturbance matrix. This process is implemented iteratively. To the best of our knowledge, this is the first targeted label attack technique. The experiments on real-world graph networks demonstrate that Graphfool can derive better performance than state-of-art techniques. Compared with the second best algorithm, Graphfool can achieve an average improvement of 11.44% in attack success rate.
Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory and time efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks.
The enormous amount of discourse taking place online poses challenges to the functioning of a civil and informed public sphere. Efforts to standardize online discourse data, such as ClaimReview, are making available a wealth of new data about potentially inaccurate claims, reviewed by third-party fact-checkers. These data could help shed light on the nature of online discourse, the role of political elites in amplifying it, and its implications for the integrity of the online information ecosystem. Unfortunately, the semi-structured nature of much of this data presents significant challenges when it comes to modeling and reasoning about online discourse. A key challenge is relation extraction, which is the task of determining the semantic relationships between named entities in a claim. Here we develop a novel supervised learning method for relation extraction that combines graph embedding techniques with path traversal on semantic dependency graphs. Our approach is based on the intuitive observation that knowledge of the entities along the path between the subject and object of a triple (e.g. Washington,_D.C.}, and United_States_of_America) provides useful information that can be leveraged for extracting its semantic relation (i.e. capitalOf). As an example of a potential application of this technique for modeling online discourse, we show that our method can be integrated into a pipeline to reason about potential misinformation claims.
Knowledge graph embedding (KGE) models learn to project symbolic entities and relations into a continuous vector space based on the observed triplets. However, existing KGE models cannot make a proper trade-off between the graph context and the model complexity, which makes them still far from satisfactory. In this paper, we propose a lightweight framework named LightCAKE for context-aware KGE. LightCAKE explicitly models the graph context without introducing redundant trainable parameters, and uses an iterative aggregation strategy to integrate the context information into the entity/relation embeddings. As a generic framework, it can be used with many simple KGE models to achieve excellent results. Finally, extensive experiments on public benchmarks demonstrate the efficiency and effectiveness of our framework.
The recently proposed EMDE (Efficient Manifold Density Estimator) model achieves state of-the-art results in session-based recommendation. In this work we explore its application to Booking Data Challenge competition. The aim of the challenge is to make the best recommendation for the next destination of a user trip, based on dataset with millions of real anonymized accommodation reservations. We achieve 2nd place in this competition. First, we use Cleora - our graph embedding method - to represent cities as a directed graph and learn their vector representation. Next, we apply EMDE to predict the next user destination based on previously visited cities and some features associated with each trip. We release the source code at: https://github.com/Synerise/booking-challenge.
Traditional computer vision approaches, based on neural networks (NN), are typically trained on a large amount of image data. By minimizing the cross-entropy loss between a prediction and a given class label, the NN and its visual embedding space are learned to fulfill a given task. However, due to the sole dependence on the image data distribution of the training domain, these models tend to fail when applied to a target domain that differs from their source domain. To learn a more robust NN to domain shifts, we propose the knowledge graph neural network (KG-NN), a neuro-symbolic approach that supervises the training using image-data-invariant auxiliary knowledge. The auxiliary knowledge is first encoded in a knowledge graph with respective concepts and their relationships, which is then transformed into a dense vector representation via an embedding method. Using a contrastive loss function, KG-NN learns to adapt its visual embedding space and thus its weights according to the image-data invariant knowledge graph embedding space. We evaluate KG-NN on visual transfer learning tasks for classification using the mini-ImageNet dataset and its derivatives, as well as road sign recognition datasets from Germany and China. The results show that a visual model trained with a knowledge graph as a trainer outperforms a model trained with cross-entropy in all experiments, in particular when the domain gap increases. Besides better performance and stronger robustness to domain shifts, these KG-NN adapts to multiple datasets and classes without suffering heavily from catastrophic forgetting.
Graph embedding is becoming an important method with applications in various areas, including social networks and knowledge graph completion. In particular, Poincar\'e embedding has been proposed to capture the hierarchical structure of graphs, and its effectiveness has been reported. However, most of the existing methods have isometric mappings in the embedding space, and the choice of the origin point can be arbitrary. This fact is not desirable when the distance from the origin is used as an indicator of hierarchy, as in the case of Poincar\'e embedding. In this paper, we propose cone embedding, embedding method in a metric cone, which solve these problems, and we gain further benefits: 1) we provide an indicator of hierarchical information that is both geometrically and intuitively natural to interpret, and 2) we can extract the hierarchical structure from a graph embedding output of other methods by learning additional one-dimensional parameters.
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these objectives are achieved, an embedding is a meaningful, understandable, compressed representations of a network that can be used for other machine learning tools such as node classification, community detection, or link prediction. The main challenge is that one needs to make sure that embeddings describe the properties of the graphs well. As a result, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we do a series of extensive experiments with selected graph embedding algorithms, both on real-world networks as well as artificially generated ones. Based on those experiments we formulate two general conclusions. First, if one needs to pick one embedding algorithm before running the experiments, then node2vec is the best choice as it performed best in our tests. Having said that, there is no single winner in all tests and, additionally, most embedding algorithms have hyperparameters that should be tuned and are randomized. Therefore, our main recommendation for practitioners is, if possible, to generate several embeddings for a problem at hand and then use a general framework that provides a tool for an unsupervised graph embedding comparison. This framework (introduced recently in the literature and easily available on GitHub repository) assigns the divergence score to embeddings to help distinguish good ones from bad ones.
Knowledge graph embedding methods learn embeddings of entities and relations in a low dimensional space which can be used for various downstream machine learning tasks such as link prediction and entity matching. Various graph convolutional network methods have been proposed which use different types of information to learn the features of entities and relations. However, these methods assign the same weight (importance) to the neighbors when aggregating the information, ignoring the role of different relations with the neighboring entities. To this end, we propose a relation-aware graph attention model that leverages relation information to compute different weights to the neighboring nodes for learning embeddings of entities and relations. We evaluate our proposed approach on link prediction and entity matching tasks. Our experimental results on link prediction on three datasets (one proprietary and two public) and results on unsupervised entity matching on one proprietary dataset demonstrate the effectiveness of the relation-aware attention.
A black-box spectral method is introduced for evaluating the adversarial robustness of a given machine learning (ML) model. Our approach, named SPADE, exploits bijective distance mapping between the input/output graphs constructed for approximating the manifolds corresponding to the input/output data. By leveraging the generalized Courant-Fischer theorem, we propose a SPADE score for evaluating the adversarial robustness of a given model, which is proved to be an upper bound of the best Lipschitz constant under the manifold setting. To reveal the most non-robust data samples highly vulnerable to adversarial attacks, we develop a spectral graph embedding procedure leveraging dominant generalized eigenvectors. This embedding step allows assigning each data sample a robustness score that can be further harnessed for more effective adversarial training. Our experiments show the proposed SPADE method leads to promising empirical results for neural network models that are adversarially trained with the MNIST and CIFAR-10 data sets.
Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The high-order information of graph can provide more abundant structure information for the representation learning of nodes. However, most self-supervised graph neural networks only use adjacency matrix as the input topology information of graph and cannot obtain too high-order information since the number of layers of graph neural network is fairly limited. If there are too many layers, the phenomenon of over smoothing will appear. Therefore how to obtain and fuse high-order information of graph by a shallow graph neural network is an important problem. In this paper, a deep graph embedding algorithm with self-supervised mechanism for community discovery is proposed. The proposed algorithm uses self-supervised mechanism and different high-order information of graph to train multiple deep graph convolution neural networks. The outputs of multiple graph convolution neural networks are fused to extract the representations of nodes which include the attribute and structure information of a graph. In addition, data augmentation and negative sampling are introduced into the training process to facilitate the improvement of embedding result. The proposed algorithm and the comparison algorithms are conducted on the five experimental data sets. The experimental results show that the proposed algorithm outperforms the comparison algorithms on the most experimental data sets. The experimental results demonstrate that the proposed algorithm is an effective algorithm for community discovery.
Model compression is an essential technique for deploying deep neural networks (DNNs) on power and memory-constrained resources. However, existing model-compression methods often rely on human expertise and focus on parameters' local importance, ignoring the rich topology information within DNNs. In this paper, we propose a novel multi-stage graph embedding technique based on graph neural networks (GNNs) to identify DNN topologies and use reinforcement learning (RL) to find a suitable compression policy. We performed resource-constrained (i.e., FLOPs) channel pruning and compared our approach with state-of-the-art model compression methods. We evaluated our method on various models from typical to mobile-friendly networks, such as ResNet family, VGG-16, MobileNet-v1/v2, and ShuffleNet. Results show that our method can achieve higher compression ratios with a minimal fine-tuning cost yet yields outstanding and competitive performance.
The area of graph embeddings is currently dominated by contrastive learning methods, which demand formulation of an explicit objective function and sampling of positive and negative examples. This creates a conceptual and computational overhead. Simple, classic unsupervised approaches like Multidimensional Scaling (MSD) or the Laplacian eigenmap skip the necessity of tedious objective optimization, directly exploiting data geometry. Unfortunately, their reliance on very costly operations such as matrix eigendecomposition make them unable to scale to large graphs that are common in today's digital world. In this paper we present Cleora: an algorithm which gets the best of two worlds, being both unsupervised and highly scalable. We show that high quality embeddings can be produced without the popular step-wise learning framework with example sampling. An intuitive learning objective of our algorithm is that a node should be similar to its neighbors, without explicitly pushing disconnected nodes apart. The objective is achieved by iterative weighted averaging of node neigbors' embeddings, followed by normalization across dimensions. Thanks to the averaging operation the algorithm makes rapid strides across the embedding space and usually reaches optimal embeddings in just a few iterations. Cleora runs faster than other state-of-the-art CPU algorithms and produces embeddings of competitive quality as measured on downstream tasks: link prediction and node classification. We show that Cleora learns a data abstraction that is similar to contrastive methods, yet at much lower computational cost. We open-source Cleora under the MIT license allowing commercial use under https://github.com/Synerise/cleora.
Knowledge graph (KG) contains well-structured external information and has shown to be effective for high-quality recommendation. However, existing KG enhanced recommendation methods have largely focused on exploring advanced neural network architectures to better investigate the structural information of KG. While for model learning, these methods mainly rely on Negative Sampling (NS) to optimize the models for both KG embedding task and recommendation task. Since NS is not robust (e.g., sampling a small fraction ofnegative instances may lose lots ofuseful information), it is reasonable to argue that these methods are insufficient to capture collaborative information among users, items, and entities. In this paper, we propose a novel Jointly Non-Sampling learning model for Knowledge graph enhanced Recommendation (JNSKR). Specifically, we first design a new efficient NS optimization algorithm for knowledge graph embedding learning. The subgraphs are then encoded by the proposed attentive neural network to better characterize user preference over items. Through novel designs of memorization strategies and joint learning framework, JNSKR not only models the fine-grained connections among users, items, and entities, but also efficiently learns model parameters from the whole training data (including all non-observed data) with a rather low time complexity. Experimental results on two public benchmarks show that JNSKR significantly outperforms the state-of-the-art methods like RippleNet and KGAT. Remarkably, JNSKR also shows significant advantages in training efficiency (about 20 times faster than KGAT), which makes it more applicable to real-world largescale systems.
In compositional zero-shot learning, the goal is to recognize unseen compositions (e.g. old dog) of observed visual primitives states (e.g. old, cute) and objects (e.g. car, dog) in the training set. This is challenging because the same state can for example alter the visual appearance of a dog drastically differently from a car. As a solution, we propose a novel graph formulation called Compositional Graph Embedding (CGE) that learns image features, compositional classifiers, and latent representations of visual primitives in an end-to-end manner. The key to our approach is exploiting the dependency between states, objects, and their compositions within a graph structure to enforce the relevant knowledge transfer from seen to unseen compositions. By learning a joint compatibility that encodes semantics between concepts, our model allows for generalization to unseen compositions without relying on an external knowledge base like WordNet. We show that in the challenging generalized compositional zero-shot setting our CGE significantly outperforms the state of the art on MIT-States and UT-Zappos. We also propose a new benchmark for this task based on the recent GQA dataset. Code is available at: https://github.com/ExplainableML/czsl