For knowledge graph completion, two major types of prediction models exist: one based on graph embeddings, and the other based on relation path rule induction. They have different advantages and disadvantages. To take advantage of both types, hybrid models have been proposed recently. One of the hybrid models, UniKER, alternately augments training data by relation path rules and trains an embedding model. Despite its high prediction accuracy, it does not take full advantage of relation path rules, as it disregards low-confidence rules in order to maintain the quality of augmented data. To mitigate this limitation, we propose transductive data augmentation by relation path rules and confidence-based weighting of augmented data. The results and analysis show that our proposed method effectively improves the performance of the embedding model by augmenting data that include true answers or entities similar to them.
The exploitation of graph structures is the key to effectively learning representations of nodes that preserve useful information in graphs. A remarkable property of graph is that a latent hierarchical grouping of nodes exists in a global perspective, where each node manifests its membership to a specific group based on the context composed by its neighboring nodes. Most prior works ignore such latent groups and nodes' membership to different groups, not to mention the hierarchy, when modeling the neighborhood structure. Thus, they fall short of delivering a comprehensive understanding of the nodes under different contexts in a graph. In this paper, we propose a novel hierarchical attentive membership model for graph embedding, where the latent memberships for each node are dynamically discovered based on its neighboring context. Both group-level and individual-level attentions are performed when aggregating neighboring states to generate node embeddings. We introduce structural constraints to explicitly regularize the inferred memberships of each node, such that a well-defined hierarchical grouping structure is captured. The proposed model outperformed a set of state-of-the-art graph embedding solutions on node classification and link prediction tasks in a variety of graphs including citation networks and social networks. Qualitative evaluations visualize the learned node embeddings along with the inferred memberships, which proved the concept of membership hierarchy and enables explainable embedding learning in graphs.
The multi-relational Knowledge Base Question Answering (KBQA) system performs multi-hop reasoning over the knowledge graph (KG) to achieve the answer. Recent approaches attempt to introduce the knowledge graph embedding (KGE) technique to handle the KG incompleteness but only consider the triple facts and neglect the significant semantic correlation between paths and multi-relational questions. In this paper, we propose a Path and Knowledge Embedding-Enhanced multi-relational Question Answering model (PKEEQA), which leverages multi-hop paths between entities in the KG to evaluate the ambipolar correlation between a path embedding and a multi-relational question embedding via a customizable path representation mechanism, benefiting for achieving more accurate answers from the perspective of both the triple facts and the extra paths. Experimental results illustrate that PKEEQA improves KBQA models' performance for multi-relational question answering with explainability to some extent derived from paths.
Knowledge graph embedding models learn the representations of entities and relations in the knowledge graphs for predicting missing links (relations) between entities. Their effectiveness are deeply affected by the ability of modeling and inferring different relation patterns such as symmetry, asymmetry, inversion, composition and transitivity. Although existing models are already able to model many of these relations patterns, transitivity, a very common relation pattern, is still not been fully supported. In this paper, we first theoretically show that the transitive relations can be modeled with projections. We then propose the Rot-Pro model which combines the projection and relational rotation together. We prove that Rot-Pro can infer all the above relation patterns. Experimental results show that the proposed Rot-Pro model effectively learns the transitivity pattern and achieves the state-of-the-art results on the link prediction task in the datasets containing transitive relations.
Unsupervised representation learning (URL), which learns compact embeddings of high-dimensional data without supervision, has made remarkable progress recently. However, the development of URLs for different requirements is independent, which limits the generalization of the algorithms, especially prohibitive as the number of tasks grows. For example, dimension reduction methods, t-SNE, and UMAP optimize pair-wise data relationships by preserving the global geometric structure, while self-supervised learning, SimCLR, and BYOL focus on mining the local statistics of instances under specific augmentations. To address this dilemma, we summarize and propose a unified similarity-based URL framework, GenURL, which can smoothly adapt to various URL tasks. In this paper, we regard URL tasks as different implicit constraints on the data geometric structure that help to seek optimal low-dimensional representations that boil down to data structural modeling (DSM) and low-dimensional transformation (LDT). Specifically, DMS provides a structure-based submodule to describe the global structures, and LDT learns compact low-dimensional embeddings with given pretext tasks. Moreover, an objective function, General Kullback-Leibler divergence (GKL), is proposed to connect DMS and LDT naturally. Comprehensive experiments demonstrate that GenURL achieves consistent state-of-the-art performance in self-supervised visual learning, unsupervised knowledge distillation (KD), graph embeddings (GE), and dimension reduction.
Knowledge graphs (KGs) consisting of a large number of triples have become widespread recently, and many knowledge graph embedding (KGE) methods are proposed to embed entities and relations of a KG into continuous vector spaces. Such embedding methods simplify the operations of conducting various in-KG tasks (e.g., link prediction) and out-of-KG tasks (e.g., question answering). They can be viewed as general solutions for representing KGs. However, existing KGE methods are not applicable to inductive settings, where a model trained on source KGs will be tested on target KGs with entities unseen during model training. Existing works focusing on KGs in inductive settings can only solve the inductive relation prediction task. They can not handle other out-of-KG tasks as general as KGE methods since they don't produce embeddings for entities. In this paper, to achieve inductive knowledge graph embedding, we propose a model MorsE, which does not learn embeddings for entities but learns transferable meta-knowledge that can be used to produce entity embeddings. Such meta-knowledge is modeled by entity-independent modules and learned by meta-learning. Experimental results show that our model significantly outperforms corresponding baselines for in-KG and out-of-KG tasks in inductive settings.
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning representations of each node. Since the formation of a graph is inevitably affected by certain sensitive node attributes, the node embeddings can inherit such sensitive information and introduce undesirable biases in downstream tasks. Most existing works impose ad-hoc constraints on the node embeddings to restrict their distributions for unbiasedness/fairness, which however compromise the utility of the resulting embeddings. In this paper, we propose a principled new way for unbiased graph embedding by learning node embeddings from an underlying bias-free graph, which is not influenced by sensitive node attributes. Motivated by this new perspective, we propose two complementary methods for uncovering such an underlying graph, with the goal of introducing minimum impact on the utility of the embeddings. Both our theoretical justification and extensive experimental comparisons against state-of-the-art solutions demonstrate the effectiveness of our proposed methods.
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms have proven to be very successful. These algorithms collect information by creating numerous random walks with a redefined number of steps. Creating random walks is the most demanding part of the embedding process. The computation demand increases with the size of the network. Moreover, for real-world networks, considering all nodes on the same footing, the abundance of low-degree nodes creates an imbalanced data problem. In this work, a computationally less intensive and node connectivity aware uniform sampling method is proposed. In the proposed method, the number of random walks is created proportionally with the degree of the node. The advantages of the proposed algorithm become more enhanced when the algorithm is applied to large graphs. A comparative study by using two networks namely CORA and CiteSeer is presented. Comparing with the fixed number of walks case, the proposed method requires 50% less computational effort to reach the same accuracy for node classification and link prediction calculations.
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions -- such as how embeddings capture different structural scales and how they should be applied for effective link prediction -- unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random-walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autocovariance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%.
Graphs are ubiquitous, and they can model unique characteristics and complex relations of real-life systems. Although using machine learning (ML) on graphs is promising, their raw representation is not suitable for ML algorithms. Graph embedding represents each node of a graph as a d-dimensional vector which is more suitable for ML tasks. However, the embedding process is expensive, and CPU-based tools do not scale to real-world graphs. In this work, we present GOSH, a GPU-based tool for embedding large-scale graphs with minimum hardware constraints. GOSH employs a novel graph coarsening algorithm to enhance the impact of updates and minimize the work for embedding. It also incorporates a decomposition schema that enables any arbitrarily large graph to be embedded with a single GPU. As a result, GOSH sets a new state-of-the-art in link prediction both in accuracy and speed, and delivers high-quality embeddings for node classification at a fraction of the time compared to the state-of-the-art. For instance, it can embed a graph with over 65 million vertices and 1.8 billion edges in less than 30 minutes on a single GPU.
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may lead to higher quality embeddings. For example, this may help one to embed the data into a given number of clusters, or to accommodate for noise that prevents one from deriving the distribution of the data over the model directly, which can then be learned more effectively. However, a general tool for integrating different prior topological knowledge into embeddings is lacking. Although differentiable topology layers have been recently developed that can (re)shape embeddings into prespecified topological models, they have two important limitations for representation learning, which we address in this paper. First, the currently suggested topological losses fail to represent simple models such as clusters and flares in a natural manner. Second, these losses neglect all original structural (such as neighborhood) information in the data that is useful for learning. We overcome these limitations by introducing a new set of topological losses, and proposing their usage as a way for topologically regularizing data embeddings to naturally represent a prespecified model. We include thorough experiments on synthetic and real data that highlight the usefulness and versatility of this approach, with applications ranging from modeling high-dimensional single-cell data, to graph embedding.
Single-cell sequencing has a significant role to explore biological processes such as embryonic development, cancer evolution, and cell differentiation. These biological properties can be presented by a two-dimensional scatter plot. However, single-cell sequencing data generally has very high dimensionality. Therefore, dimensionality reduction should be used to process the high dimensional sequencing data for 2D visualization and subsequent biological analysis. The traditional dimensionality reduction methods, which do not consider the structure characteristics of single-cell sequencing data, are difficult to reveal the data structure in the 2D representation. In this paper, we develop a 2D feature representation method based on graph convolutional networks (GCN) for the visualization of single-cell data, termed single-cell sequencing graph embedding networks (SGEN). This method constructs the graph by the similarity relationship between cells and adopts GCN to analyze the neighbor embedding information of samples, which makes the similar cell closer to each other on the 2D scatter plot. The results show SGEN achieves obvious 2D distribution and preserves the high-dimensional relationship of different cells. Meanwhile, similar cell clusters have spatial continuity rather than relying heavily on random initialization, which can reflect the trajectory of cell development in this scatter plot.
Predicting the next place to visit is a key in human mobility behavior modeling, which plays a significant role in various fields, such as epidemic control, urban planning, traffic management, and travel recommendation. To achieve this, one typical solution is designing modules based on RNN to capture their preferences to various locations. Although these RNN-based methods can effectively learn individual's hidden personalized preferences to her visited places, the interactions among users can only be weakly learned through the representations of locations. Targeting this, we propose an end-to-end framework named personalized and group preference guided network (PG$^2$Net), considering the users' preferences to various places at both individual and collective levels. Specifically, PG$^2$Net concatenates Bi-LSTM and attention mechanism to capture each user's long-term mobility tendency. To learn population's group preferences, we utilize spatial and temporal information of the visitations to construct a spatio-temporal dependency module. We adopt a graph embedding method to map users' trajectory into a hidden space, capturing their sequential relation. In addition, we devise an auxiliary loss to learn the vectorial representation of her next location. Experiment results on two Foursquare check-in datasets and one mobile phone dataset indicate the advantages of our model compared to the state-of-the-art baselines. Source codes are available at https://github.com/urbanmobility/PG2Net.
Graph embedding maps a graph into a convenient vector-space representation for graph analysis and machine learning applications. Many graph embedding methods hinge on a sampling of context nodes based on random walks. However, random walks can be a biased sampler due to the structural properties of graphs. Most notably, random walks are biased by the degree of each node, where a node is sampled proportionally to its degree. The implication of such biases has not been clear, particularly in the context of graph representation learning. Here, we investigate the impact of the random walks' bias on graph embedding and propose residual2vec, a general graph embedding method that can debias various structural biases in graphs by using random graphs. We demonstrate that this debiasing not only improves link prediction and clustering performance but also allows us to explicitly model salient structural properties in graph embedding.
Identifying vulnerabilities in the source code is essential to protect the software systems from cyber security attacks. It, however, is also a challenging step that requires specialized expertise in security and code representation. To this end, we aim to develop a general, practical, and programming language-independent model capable of running on various source codes and libraries without difficulty. Therefore, we consider vulnerability detection as an inductive text classification problem and propose ReGVD, a simple yet effective graph neural network-based model for the problem. In particular, ReGVD views each raw source code as a flat sequence of tokens to build a graph, wherein node features are initialized by only the token embedding layer of a pre-trained programming language (PL) model. ReGVD then leverages residual connection among GNN layers and examines a mixture of graph-level sum and max poolings to return a graph embedding for the source code. ReGVD outperforms the existing state-of-the-art models and obtains the highest accuracy on the real-world benchmark dataset from CodeXGLUE for vulnerability detection. Our code is available at: \url{https://github.com/daiquocnguyen/GNN-ReGVD}.
Graph embedding techniques have attracted growing interest since they convert the graph data into continuous and low-dimensional space. Effective graph analytic provides users a deeper understanding of what is behind the data and thus can benefit a variety of machine learning tasks. With the current scale of real-world applications, most graph analytic methods suffer high computation and space costs. These methods and systems can process a network with thousands to a few million nodes. However, scaling to large-scale networks remains a challenge. The complexity of training graph embedding system requires the use of existing accelerators such as GPU. In this paper, we introduce a hybrid CPU-GPU framework that addresses the challenges of learning embedding of large-scale graphs. The performance of our method is compared qualitatively and quantitatively with the existing embedding systems on common benchmarks. We also show that our system can scale training to datasets with an order of magnitude greater than a single machine's total memory capacity. The effectiveness of the learned embedding is evaluated within multiple downstream applications. The experimental results indicate the effectiveness of the learned embedding in terms of performance and accuracy.
Given a node-attributed graph, how can we efficiently represent it with few numerical features that expressively reflect its topology and attribute information? We propose A-DOGE, for Attributed DOS-based Graph Embedding, based on density of states (DOS, a.k.a. spectral density) to tackle this problem. A-DOGE is designed to fulfill a long desiderata of desirable characteristics. Most notably, it capitalizes on efficient approximation algorithms for DOS, that we extend to blend in node labels and attributes for the first time, making it fast and scalable for large attributed graphs and graph databases. Being based on the entire eigenspectrum of a graph, A-DOGE can capture structural and attribute properties at multiple ("glocal") scales. Moreover, it is unsupervised (i.e. agnostic to any specific objective) and lends itself to various interpretations, which makes it is suitable for exploratory graph mining tasks. Finally, it processes each graph independent of others, making it amenable for streaming settings as well as parallelization. Through extensive experiments, we show the efficacy and efficiency of A-DOGE on exploratory graph analysis and graph classification tasks, where it significantly outperforms unsupervised baselines and achieves competitive performance with modern supervised GNNs, while achieving the best trade-off between accuracy and runtime.
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of \textit{cellular sheaves}: a knowledge graph embedding can be described as an approximate global section of an appropriate \textit{knowledge sheaf} over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.
Recently, deep learning has achieved promising results in the calculation of Estimated Time of Arrival (ETA), which is considered as predicting the travel time from the start point to a certain place along a given path. ETA plays an essential role in intelligent taxi services or automotive navigation systems. A common practice is to use embedding vectors to represent the elements of a road network, such as road segments and crossroads. Road elements have their own attributes like length, presence of crosswalks, lanes number, etc. However, many links in the road network are traversed by too few floating cars even in large ride-hailing platforms and affected by the wide range of temporal events. As the primary goal of the research, we explore the generalization ability of different spatial embedding strategies and propose a two-stage approach to deal with such problems.
In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We proposed a hybrid pointer network (HPN) to solve the travelling salesman problem trained by reinforcement learning. Furthermore, HPN builds upon graph pointer networks which is an extension of pointer networks with an additional graph embedding layer. HPN outperforms the graph pointer network in solution quality due to the hybrid encoder, which provides our model with a verity encoding type, allowing our model to converge to a better policy. Our network significantly outperforms the original graph pointer network for small and large-scale problems increasing its performance for TSP50 from 5.959 to 5.706 without utilizing 2opt, Pointer networks, Attention model, and a wide range of models, producing results comparable to highly tuned and specialized algorithms. We make our data, models, and code publicly available [2].