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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
Network seeding for efficient information diffusion over time-varying graphs~(TVGs) is a challenging task with many real-world applications. There are several ways to model this spatio-temporal influence maximization problem, but the ultimate goal is to determine the best moment for a node to start the diffusion process. In this context, we propose Spatio-Temporal Influence Maximization~(STIM), a model trained with Reinforcement Learning and Graph Embedding over a set of artificial TVGs that is capable of learning the temporal behavior and connectivity pattern of each node, allowing it to predict the best moment to start a diffusion through the TVG. We also develop a special set of artificial TVGs used for training that simulate a stochastic diffusion process in TVGs, showing that the STIM network can learn an efficient policy even over a non-deterministic environment. STIM is also evaluated with a real-world TVG, where it also manages to efficiently propagate information through the nodes. Finally, we also show that the STIM model has a time complexity of $O(|E|)$. STIM, therefore, presents a novel approach for efficient information diffusion in TVGs, being highly versatile, where one can change the goal of the model by simply changing the adopted reward function.
At online retail platforms, it is crucial to actively detect the risks of transactions to improve customer experience and minimize financial loss. In this work, we propose xFraud, an explainable fraud transaction prediction framework which is mainly composed of a detector and an explainer. The xFraud detector can effectively and efficiently predict the legitimacy of incoming transactions. Specifically, it utilizes a heterogeneous graph neural network to learn expressive representations from the informative heterogeneously typed entities in the transaction logs. The explainer in xFraud can generate meaningful and human-understandable explanations from graphs to facilitate further processes in the business unit. In our experiments with xFraud on real transaction networks with up to 1.1 billion nodes and 3.7 billion edges, xFraud is able to outperform various baseline models in many evaluation metrics while remaining scalable in distributed settings. In addition, we show that xFraud explainer can generate reasonable explanations to significantly assist the business analysis via both quantitative and qualitative evaluations.
The widespread adoption of machine learning (ML) techniques and the extensive expertise required to apply them have led to increased interest in automated ML solutions that reduce the need for human intervention. One of the main challenges in applying ML to previously unseen problems is algorithm selection - the identification of high-performing algorithm(s) for a given dataset, task, and evaluation measure. This study addresses the algorithm selection challenge for data clustering, a fundamental task in data mining that is aimed at grouping similar objects. We present MARCO-GE, a novel meta-learning approach for the automated recommendation of clustering algorithms. MARCO-GE first transforms datasets into graphs and then utilizes a graph convolutional neural network technique to extract their latent representation. Using the embedding representations obtained, MARCO-GE trains a ranking meta-model capable of accurately recommending top-performing algorithms for a new dataset and clustering evaluation measure. Extensive evaluation on 210 datasets, 13 clustering algorithms, and 10 clustering measures demonstrates the effectiveness of our approach and its superiority in terms of predictive and generalization performance over state-of-the-art clustering meta-learning approaches.
We develop a fused matrix multiplication kernel that unifies sampled dense-dense matrix multiplication and sparse-dense matrix multiplication under a single operation called FusedMM. By using user-defined functions, FusedMM can capture almost all computational patterns needed by popular graph embedding and GNN approaches. FusedMM is an order of magnitude faster than its equivalent kernels in Deep Graph Library. The superior performance of FusedMM comes from the low-level vectorized kernels, a suitable load balancing scheme and an efficient utilization of the memory bandwidth. FusedMM can tune its performance using a code generator and perform equally well on Intel, AMD and ARM processors. FusedMM speeds up an end-to-end graph embedding algorithm by up to 28x on different processors.
Link scheduling in device-to-device (D2D) networks is usually formulated as a non-convex combinatorial problem, which is generally NP-hard and difficult to get the optimal solution. Traditional methods to solve this problem are mainly based on mathematical optimization techniques, where accurate channel state information (CSI), usually obtained through channel estimation and feedback, is needed. To overcome the high computational complexity of the traditional methods and eliminate the costly channel estimation stage, machine leaning (ML) has been introduced recently to address the wireless link scheduling problems. In this paper, we propose a novel graph embedding based method for link scheduling in D2D networks. We first construct a fully-connected directed graph for the D2D network, where each D2D pair is a node while interference links among D2D pairs are the edges. Then we compute a low-dimensional feature vector for each node in the graph. The graph embedding process is based on the distances of both communication and interference links, therefore without requiring the accurate CSI. By utilizing a multi-layer classifier, a scheduling strategy can be learned in a supervised manner based on the graph embedding results for each node. We also propose an unsupervised manner to train the graph embedding based method to further reinforce the scalability and generalizability and develop a K-nearest neighbor graph representation method to reduce the computational complexity. Extensive simulation demonstrates that the proposed method is near-optimal compared with the existing state-of-art methods but is with only hundreds of training samples. It is also competitive in terms of scalability and generalizability to more complicated scenarios.