Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the size of the graphs. In this paper, we propose a new family of global alignment graph kernels, which take into account the global properties of graphs by using geometric node embeddings and an associated node transportation based on earth mover's distance. Compared to existing global kernels, the proposed kernel is positive-definite. Our graph kernel is obtained by defining a distribution over \emph{random graphs}, which can naturally yield random feature approximations. The random feature approximations lead to our graph embeddings, which is named as "random graph embeddings" (RGE). In particular, RGE is shown to achieve \emph{(quasi-)linear scalability} with respect to the number and the size of the graphs. The experimental results on nine benchmark datasets demonstrate that RGE outperforms or matches twelve state-of-the-art graph classification algorithms.
Graph is a natural representation of data for a variety of real-word applications, such as knowledge graph mining, social network analysis and biological network comparison. For these applications, graph embedding is crucial as it provides vector representations of the graph. One limitation of existing graph embedding methods is that their embedding optimization procedures are disconnected from the target application. In this paper, we propose a novel approach, namely Customized Graph Embedding (CGE) to tackle this problem. The CGE algorithm learns customized vector representations of graph nodes by differentiating the importance of distinct graph paths automatically for a specific application. Extensive experiments were carried out on a diverse set of node classification datasets, which demonstrate strong performances of CGE and provide deep insights into the model.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model -- namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE) -- which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
As an efficient model for knowledge organization, the knowledge graph has been widely adopted in several fields, e.g., biomedicine, sociology, and education. And there is a steady trend of learning embedding representations of knowledge graphs to facilitate knowledge graph construction and downstream tasks. In general, knowledge graph embedding techniques aim to learn vectorized representations which preserve the structural information of the graph. And conventional embedding learning models rely on structural relationships among entities and relations. However, in educational knowledge graphs, structural relationships are not the focus. Instead, rich literals of the graphs are more valuable. In this paper, we focus on this problem and propose a novel model for embedding learning of educational knowledge graphs. Our model considers both structural and literal information and jointly learns embedding representations. Three experimental graphs were constructed based on an educational knowledge graph which has been applied in real-world teaching. We conducted two experiments on the three graphs and other common benchmark graphs. The experimental results proved the effectiveness of our model and its superiority over other baselines when processing educational knowledge graphs.
This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that partitions the computation tasks of a stream processing graph onto computing devices must simultaneously balance workload distribution and minimize communication. Since this problem of graph partitioning is known to be NP-complete yet crucial to practical streaming systems, many heuristic-based algorithms have been developed to find reasonably good solutions. In this paper, we present a graph-aware encoder-decoder framework to learn a generalizable resource allocation strategy that can properly distribute computation tasks of stream processing graphs unobserved from training data. We, for the first time, propose to leverage graph embedding to learn the structural information of the stream processing graphs. Jointly trained with the graph-aware decoder using deep reinforcement learning, our approach can effectively find optimized solutions for unseen graphs. Our experiments show that the proposed model outperforms both METIS, a state-of-the-art graph partitioning algorithm, and an LSTM-based encoder-decoder model, in about 70% of the test cases.
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and the traditional \textit{Skip-Gram} model to capture center-context node relationships. In this paper, we emphasize on exponential family distributions to capture rich interaction patterns between nodes in random walk sequences. We introduce the generic \textit{exponential family graph embedding} model, that generalizes random walk-based network representation learning techniques to exponential family conditional distributions. We study three particular instances of this model, analyzing their properties and showing their relationship to existing unsupervised learning models. Our experimental evaluation on real-world datasets demonstrates that the proposed techniques outperform well-known baseline methods in two downstream machine learning tasks.
Knowledge Graph (KG) embedding has attracted more attention in recent years. Most KG embedding models learn from time-unaware triples. However, the inclusion of temporal information beside triples would further improve the performance of a KGE model. In this regard, we propose ATiSE, a temporal KG embedding model which incorporates time information into entity/relation representations by using Additive Time Series decomposition. Moreover, considering the temporal uncertainty during the evolution of entity/relation representations over time, we map the representations of temporal KGs into the space of multi-dimensional Gaussian distributions. The mean of each entity/relation embedding at a time step shows the current expected position, whereas its covariance (which is temporally stationary) represents its temporal uncertainty. Experimental results show that ATiSE chieves the state-of-the-art on link prediction over four temporal KGs.
The dominant paradigm for relation prediction in knowledge graphs involves learning and operating on latent representations (i.e., embeddings) of entities and relations. However, these embedding-based methods do not explicitly capture the compositional logical rules underlying the knowledge graph, and they are limited to the transductive setting, where the full set of entities must be known during training. Here, we propose a graph neural network based relation prediction framework, GraIL, that reasons over local subgraph structures and has a strong inductive bias to learn entity-independent relational semantics. Unlike embedding-based models, GraIL is naturally inductive and can generalize to unseen entities and graphs after training. We provide theoretical proof and strong empirical evidence that GraIL can represent a useful subset of first-order logic and show that GraIL outperforms existing rule-induction baselines in the inductive setting. We also demonstrate significant gains obtained by ensembling GraIL with various knowledge graph embedding methods in the transductive setting, highlighting the complementary inductive bias of our method.
Knowledge graph (KG) embedding is well-known in learning representations of KGs. Many models have been proposed to learn the interactions between entities and relations of the triplets. However, long-term information among multiple triplets is also important to KG. In this work, based on the relational paths, which are composed of a sequence of triplets, we define the Interstellar as a recurrent neural architecture search problem for the short-term and long-term information along the paths. First, we analyze the difficulty of using a unified model to work as the Interstellar. Then, we propose to search for recurrent architecture as the Interstellar for different KG tasks. A case study on synthetic data illustrates the importance of the defined search problem. Experiments on real datasets demonstrate the effectiveness of the searched models and the efficiency of the proposed hybrid-search algorithm.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to constrained combinatorial optimization problems such as the TSP with time windows, we train hierarchical GPNs (HGPNs) using RL, which learns a hierarchical policy to find an optimal city permutation under constraints. Each layer of the hierarchy is designed with a separate reward function, resulting in stable training. Our results demonstrate that GPNs trained on small-scale TSP50/100 problems generalize well to larger-scale TSP500/1000 problems, with shorter tour lengths and faster computational times. We verify that for constrained TSP problems such as the TSP with time windows, the feasible solutions found via hierarchical RL training outperform previous baselines. In the spirit of reproducible research we make our data, models, and code publicly available.
This paper studies the problem of predicting missing relationships between entities in knowledge graphs through learning their representations. Currently, the majority of existing link prediction models employ simple but intuitive scoring functions and relatively small embedding size so that they could be applied to large-scale knowledge graphs. However, these properties also restrict the ability to learn more expressive and robust features. Therefore, diverging from most of the prior works which focus on designing new objective functions, we propose, DeCom, a simple but effective mechanism to boost the performance of existing link predictors such as DistMult, ComplEx, etc, through extracting more expressive features while preventing overfitting by adding just a few extra parameters. Specifically, embeddings of entities and relationships are first decompressed to a more expressive and robust space by decompressing functions, then knowledge graph embedding models are trained in this new feature space. Experimental results on several benchmark knowledge graphs and advanced link prediction systems demonstrate the generalization and effectiveness of our method. Especially, RESCAL + DeCom achieves state-of-the-art performance on the FB15k-237 benchmark across all evaluation metrics. In addition, we also show that compared with DeCom, explicitly increasing the embedding size significantly increase the number of parameters but could not achieve promising performance improvement.
Time series modeling has attracted extensive research efforts; however, achieving both reliable efficiency and interpretability from a unified model still remains a challenging problem. Among the literature, shapelets offer interpretable and explanatory insights in the classification tasks, while most existing works ignore the differing representative power at different time slices, as well as (more importantly) the evolution pattern of shapelets. In this paper, we propose to extract time-aware shapelets by designing a two-level timing factor. Moreover, we define and construct the shapelet evolution graph, which captures how shapelets evolve over time and can be incorporated into the time series embeddings by graph embedding algorithms. To validate whether the representations obtained in this way can be applied effectively in various scenarios, we conduct experiments based on three public time series datasets, and two real-world datasets from different domains. Experimental results clearly show the improvements achieved by our approach compared with 17 state-of-the-art baselines.
Graph Convolutional Networks (GCNs) have recently been shown to be quite successful in modeling graph-structured data. However, the primary focus has been on handling simple undirected graphs. Multi-relational graphs are a more general and prevalent form of graphs where each edge has a label and direction associated with it. Most of the existing approaches to handle such graphs suffer from over-parameterization and are restricted to learning representations of nodes only. In this paper, we propose CompGCN, a novel Graph Convolutional framework which jointly embeds both nodes and relations in a relational graph. CompGCN leverages a variety of entity-relation composition operations from Knowledge Graph Embedding techniques and scales with the number of relations. It also generalizes several of the existing multi-relational GCN methods. We evaluate our proposed method on multiple tasks such as node classification, link prediction, and graph classification, and achieve demonstrably superior results. We make the source code of CompGCN available to foster reproducible research.
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them tend to be sparse with very few facts per entity. In the first part of the thesis, we propose two solutions to alleviate this problem: (1) KG Canonicalization, i.e., identifying and merging duplicate entities in a KG, (2) Relation Extraction which involves automating the process of extracting semantic relationships between entities from unstructured text. Traditional Neural Networks like CNNs and RNNs are constrained to handle Euclidean data. However, graphs in Natural Language Processing (NLP) are prominent. Recently, Graph Convolutional Networks (GCNs) have been proposed to address this shortcoming and have been successfully applied for several problems. In the second part of the thesis, we utilize GCNs for Document Timestamping problem and for learning word embeddings using dependency context of a word instead of sequential context. In this third part of the thesis, we address two limitations of existing GCN models, i.e., (1) The standard neighborhood aggregation scheme puts no constraints on the number of nodes that can influence the representation of a target node. This leads to a noisy representation of hub-nodes which coves almost the entire graph in a few hops. (2) Most of the existing GCN models are limited to handle undirected graphs. However, a more general and pervasive class of graphs are relational graphs where each edge has a label and direction associated with it. Existing approaches to handle such graphs suffer from over-parameterization and are restricted to learning representation of nodes only.
Knowledge graph embedding, which projects symbolic entities and relations into continuous vector spaces, is gaining increasing attention. Previous methods allow a single static embedding for each entity or relation, ignoring their intrinsic contextual nature, i.e., entities and relations may appear in different graph contexts, and accordingly, exhibit different properties. This work presents Contextualized Knowledge Graph Embedding (CoKE), a novel paradigm that takes into account such contextual nature, and learns dynamic, flexible, and fully contextualized entity and relation embeddings. Two types of graph contexts are studied: edges and paths, both formulated as sequences of entities and relations. CoKE takes a sequence as input and uses a Transformer encoder to obtain contextualized representations. These representations are hence naturally adaptive to the input, capturing contextual meanings of entities and relations therein. Evaluation on a wide variety of public benchmarks verifies the superiority of CoKE in link prediction and path query answering. It performs consistently better than, or at least equally well as current state-of-the-art in almost every case, in particular offering an absolute improvement of 21.0% in H@10 on path query answering. Our code is available at \url{https://github.com/PaddlePaddle/Research/tree/master/KG/CoKE}.
Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream applications such as link prediction and anomaly detection, it is essential for such networks to be transferred into a low dimensional space. Recently, network embedding, a technique that converts a large graph into a low-dimensional representation, has become increasingly popular due to its strength in preserving the structure of a network. Efficient dynamic network embedding, however, has not yet been fully explored. In this paper, we present a dynamic network embedding method that integrates the history of nodes over time into the current state of nodes. The key contribution of our work is 1) generating dynamic network embedding by combining both dynamic and static node information 2) tracking history of neighbors of nodes using LSTM 3) significantly decreasing the time and memory by training an autoencoder LSTM model using temporal walks rather than adjacency matrices of graphs which are the common practice. We evaluate our method in multiple applications such as anomaly detection, link prediction and node classification in datasets from various domains.
Relational data mining is becoming ubiquitous in many fields of study. It offers insights into behaviour of complex, real-world systems which cannot be modeled directly using propositional learning. We propose Symbolic Graph Embedding (SGE), an algorithm aimed to learn symbolic node representations. Built on the ideas from the field of inductive logic programming, SGE first samples a given node's neighborhood and interprets it as a transaction database, which is used for frequent pattern mining to identify logical conjuncts of items that co-occur frequently in a given context. Such patterns are in this work used as features to represent individual nodes, yielding interpretable, symbolic node embeddings. The proposed SGE approach on a venue classification task outperforms shallow node embedding methods such as DeepWalk, and performs similarly to metapath2vec, a black-box representation learner that can exploit node and edge types in a given graph. The proposed SGE approach performs especially well when small amounts of data are used for learning, scales to graphs with millions of nodes and edges, and can be run on an of-the-shelf laptop.
Knowledge graphs (KGs) have proven to be effective for high-quality recommendation, where the connectivities between users and items provide rich and complementary information to user-item interactions. Most existing methods, however, are insufficient to exploit the KGs for capturing user preferences, as they either represent the user-item connectivities via paths with limited expressiveness or implicitly model them by propagating information over the entire KG with inevitable noise. In this paper, we design a novel hierarchical attentive knowledge graph embedding (HAKG) framework to exploit the KGs for effective recommendation. Specifically, HAKG first extracts the expressive subgraphs that link user-item pairs to characterize their connectivities, which accommodate both the semantics and topology of KGs. The subgraphs are then encoded via a hierarchical attentive subgraph encoding to generate effective subgraph embeddings for enhanced user preference prediction. Extensive experiments show the superiority of HAKG against state-of-the-art recommendation methods, as well as its potential in alleviating the data sparsity issue.
Recently, recommendation according to sequential user behaviors has shown promising results in many application scenarios. Generally speaking, real-world sequential user behaviors usually reflect a hybrid of sequential influences and association relationships. However, most existing sequential recommendation methods mainly concentrate on sequential relationships while ignoring association relationships. In this paper, we propose a unified method that incorporates item association and sequential relationships for sequential recommendation. Specifically, we encode the item association as relations in item co-occurrence graph and mine it through graph embedding by GCNs. In the meanwhile, we model the sequential relationships through a widely used RNNs based sequential recommendation method named GRU4Rec. The two parts are connected into an end-to-end network with cascading style, which guarantees that representations for item associations and sequential relationships are learned simultaneously and make the learning process maintain low complexity. We perform extensive experiments on three widely used real-world datasets: TaoBao, Amazon Instant Video and Amazon Cell Phone and Accessories. Comprehensive results have shown that the proposed method outperforms several state-of-the-art methods. Furthermore, a qualitative analysis is also provided to encourage a better understanding about association relationships in sequential recommendation and illustrate the performance gain is exactly from item association.