Detecting the Maximum Common Subgraph (MCS) between two input graphs is fundamental for applications in drug synthesis, malware detection, cloud computing, etc. However, MCS computation is NP-hard, and state-of-the-art MCS solvers rely on heuristic search algorithms which in practice cannot find good solution for large graph pairs given a limited computation budget. We propose GLSearch, a Graph Neural Network (GNN) based learning to search model. Our model is built upon the branch and bound algorithm, which selects one pair of nodes from the two input graphs to expand at a time. Instead of using heuristics, we propose a novel GNN-based Deep Q-Network (DQN) to select the node pair, allowing the search process faster and more adaptive. To further enhance the training of DQN, we leverage the search process to provide supervision in a pre-training stage and guide our agent during an imitation learning stage. Experiments on synthetic and real-world large graph pairs demonstrate that our model learns a search strategy that is able to detect significantly larger common subgraphs given the same computation budget. Our GLSearch can be potentially extended to solve many other combinatorial problems with constraints on graphs.
Point-of-Interest (POI) recommendation is one of the most important location-based services helping people discover interesting venues or services. However, the extreme user-POI matrix sparsity and the varying spatio-temporal context pose challenges for POI systems, which affects the quality of POI recommendations. To this end, we propose a translation-based relation embedding for POI recommendation. Our approach encodes the temporal and geographic information, as well as semantic contents effectively in a low-dimensional relation space by using Knowledge Graph Embedding techniques. To further alleviate the issue of user-POI matrix sparsity, a combined matrix factorization framework is built on a user-POI graph to enhance the inference of dynamic personal interests by exploiting the side-information. Experiments on two real-world datasets demonstrate the effectiveness of our proposed model.
A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we propose a new model named Metapath Aggregated Graph Neural Network (MAGNN) to boost the final performance. Specifically, MAGNN employs three major components, i.e., the node content transformation to encapsulate input node attributes, the intra-metapath aggregation to incorporate intermediate semantic nodes, and the inter-metapath aggregation to combine messages from multiple metapaths. Extensive experiments on three real-world heterogeneous graph datasets for node classification, node clustering, and link prediction show that MAGNN achieves more accurate prediction results than state-of-the-art baselines.
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.
Knowledge Graphs (KGs) have found many applications in industry and academic settings, which in turn, have motivated considerable research efforts towards large-scale information extraction from a variety of sources. Despite such efforts, it is well known that even state-of-the-art KGs suffer from incompleteness. Link Prediction (LP), the task of predicting missing facts among entities already a KG, is a promising and widely studied task aimed at addressing KG incompleteness. Among the recent LP techniques, those based on KG embeddings have achieved very promising performances in some benchmarks. Despite the fast growing literature in the subject, insufficient attention has been paid to the effect of the various design choices in those methods. Moreover, the standard practice in this area is to report accuracy by aggregating over a large number of test facts in which some entities are over-represented; this allows LP methods to exhibit good performance by just attending to structural properties that include such entities, while ignoring the remaining majority of the KG. This analysis provides a comprehensive comparison of embedding-based LP methods, extending the dimensions of analysis beyond what is commonly available in the literature. We experimentally compare effectiveness and efficiency of 16 state-of-the-art methods, consider a rule-based baseline, and report detailed analysis over the most popular benchmarks in the literature.
The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ (or a Gumbel-Max variable $i$) in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and graph embedding require to generate $k$ independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large $k$ (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, \emph{FastGM}, that reduces the time complexity from $O(kn^+)$ to $O(k \ln k + n^+)$, where $n^+$ is the number of positive elements in the vector of interest. Instead of computing $k$ independent Gumbel random variables directly, we find that there exists a technique to generate these variables in descending order. Using this technique, our method FastGM computes variables $g_i+\ln v_i$ for all positive elements $i$ in descending order. As a result, FastGM significantly reduces the computation time because we can stop the procedure of Gumbel random variables computing for many elements especially for those with small weights. Experiments on a variety of real-world datasets show that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy and incurring additional expenses.
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph is directed or not. Most studies ignore the directionality, so as to learn high-quality representations optimized for node classification. On the other hand, studies that capture directionality are usually effective on link prediction but do not perform well on other tasks. This preliminary study presents a novel text-enriched, direction-aware algorithm called DIAGRAM , based on a carefully designed multi-objective model to learn embeddings that preserve the direction of edges, textual features and graph context of nodes. As a result, our algorithm does not have to trade one property for another and jointly learns high-quality representations for multiple network analysis tasks. We empirically show that DIAGRAM significantly outperforms six state-of-the-art baselines, both direction-aware and oblivious ones,on link prediction and network reconstruction experiments using two popular datasets. It also achieves a comparable performance on node classification experiments against these baselines using the same datasets.
There is an emerging trend of embedding knowledge graphs (KGs) in continuous vector spaces in order to use those for machine learning tasks. Recently, many knowledge graph embedding (KGE) models have been proposed that learn low dimensional representations while trying to maintain the structural properties of the KGs such as the similarity of nodes depending on their edges to other nodes. KGEs can be used to address tasks within KGs such as the prediction of novel links and the disambiguation of entities. They can also be used for downstream tasks like question answering and fact-checking. Overall, these tasks are relevant for the semantic web community. Despite their popularity, the reproducibility of KGE experiments and the transferability of proposed KGE models to research fields outside the machine learning community can be a major challenge. Therefore, we present the KEEN Universe, an ecosystem for knowledge graph embeddings that we have developed with a strong focus on reproducibility and transferability. The KEEN Universe currently consists of the Python packages PyKEEN (Python KnowlEdge EmbeddiNgs), BioKEEN (Biological KnowlEdge EmbeddiNgs), and the KEEN Model Zoo for sharing trained KGE models with the community.
A collaborative network is a social network that is comprised of experts who cooperate with each other to fulfill a special goal. Analyzing this network yields meaningful information about the expertise of these experts and their subject areas. To perform the analysis, graph embedding techniques have emerged as an effective and promising tool. Graph embedding attempts to represent graph nodes as low-dimensional vectors. In this paper, we propose a graph embedding method, called ExEm, that uses dominating-set theory and deep learning approaches to capture node representations. ExEm finds dominating nodes of the collaborative network and constructs intelligent random walks that comprise of at least two dominating nodes. One dominating node should appear at the beginning of each path sampled to characterize the local neighborhoods. Moreover, the second dominating node reflects the global structure information. To learn the node embeddings, ExEm exploits three embedding methods including Word2vec, fastText and the concatenation of these two. The final result is the low-dimensional vectors of experts, called expert embeddings. The extracted expert embeddings can be applied to many applications. In order to extend these embeddings into the expert recommendation system, we introduce a novel strategy that uses expert vectors to calculate experts' scores and recommend experts. At the end, we conduct extensive experiments to validate the effectiveness of ExEm through assessing its performance over the multi-label classification, link prediction, and recommendation tasks on common datasets and our collected data formed by crawling the vast author Scopus profiles. The experiments show that ExEm outperforms the baselines especially in dense networks.
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we propose diffusion graphs as a method to rapidly generate vertex sequences for network embedding. Its computational efficiency is superior to previous methods due to simpler sequence generation, and it produces more accurate results. In experiments, we found that the performance relative to other methods improves with increasing edge density in the graph. In a community detection task, clustering nodes in the embedding space produces better results compared to other sequence-based embedding methods.
Knowledge graph embedding methods learn continuous vector representations for entities in knowledge graphs and have been used successfully in a large number of applications. We present a novel and scalable paradigm for the computation of knowledge graph embeddings, which we dub PYKE . Our approach combines a physical model based on Hooke's law and its inverse with ideas from simulated annealing to compute embeddings for knowledge graphs efficiently. We prove that PYKE achieves a linear space complexity. While the time complexity for the initialization of our approach is quadratic, the time complexity of each of its iterations is linear in the size of the input knowledge graph. Hence, PYKE's overall runtime is close to linear. Consequently, our approach easily scales up to knowledge graphs containing millions of triples. We evaluate our approach against six state-of-the-art embedding approaches on the DrugBank and DBpedia datasets in two series of experiments. The first series shows that the cluster purity achieved by PYKE is up to 26% (absolute) better than that of the state of art. In addition, PYKE is more than 22 times faster than existing embedding solutions in the best case. The results of our second series of experiments show that PYKE is up to 23% (absolute) better than the state of art on the task of type prediction while maintaining its superior scalability. Our implementation and results are open-source and are available at http://github.com/dice-group/PYKE.
Graph and language embedding models are becoming commonplace in large scale analyses given their ability to represent complex sparse data densely in low-dimensional space. Integrating these models' complementary relational and communicative data may be especially helpful if predicting rare events or classifying members of hidden populations - tasks requiring huge and sparse datasets for generalizable analyses. For example, due to social stigma and comorbidities, mental health support groups often form in amorphous online groups. Predicting suicidality among individuals in these settings using standard network analyses is prohibitive due to resource limits (e.g., memory), and adding auxiliary data like text to such models exacerbates complexity- and sparsity-related issues. Here, I show how merging graph and language embedding models (metapath2vec and doc2vec) avoids these limits and extracts unsupervised clustering data without domain expertise or feature engineering. Graph and language distances to a suicide support group have little correlation (\r{ho} < 0.23), implying the two models are not embedding redundant information. When used separately to predict suicidality among individuals, graph and language data generate relatively accurate results (69% and 76%, respectively); however, when integrated, both data produce highly accurate predictions (90%, with 10% false-positives and 12% false-negatives). Visualizing graph embeddings annotated with predictions of potentially suicidal individuals shows the integrated model could classify such individuals even if they are positioned far from the support group. These results extend research on the importance of simultaneously analyzing behavior and language in massive networks and efforts to integrate embedding models for different kinds of data when predicting and classifying, particularly when they involve rare events.
In this paper, we focus on graph representation learning of heterogeneous information network (HIN), in which various types of vertices are connected by various types of relations. Most of the existing methods conducted on HIN revise homogeneous graph embedding models via meta-paths to learn low-dimensional vector space of HIN. In this paper, we propose a novel Heterogeneous Graph Structural Attention Neural Network (HetSANN) to directly encode structural information of HIN without meta-path and achieve more informative representations. With this method, domain experts will not be needed to design meta-path schemes and the heterogeneous information can be processed automatically by our proposed model. Specifically, we implicitly represent heterogeneous information using the following two methods: 1) we model the transformation between heterogeneous vertices through a projection in low-dimensional entity spaces; 2) afterwards, we apply the graph neural network to aggregate multi-relational information of projected neighborhood by means of attention mechanism. We also present three extensions of HetSANN, i.e., voices-sharing product attention for the pairwise relationships in HIN, cycle-consistency loss to retain the transformation between heterogeneous entity spaces, and multi-task learning with full use of information. The experiments conducted on three public datasets demonstrate that our proposed models achieve significant and consistent improvements compared to state-of-the-art solutions.
Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present a novel method to calibrate a model when ground truth negatives are not available, which is the usual case in knowledge graphs. We propose to use Platt scaling and isotonic regression alongside our method. Experiments on three datasets with ground truth negatives show our contribution leads to well-calibrated models when compared to the gold standard of using negatives. We get significantly better results than the uncalibrated models from all calibration methods. We show isotonic regression offers the best the performance overall, not without trade-offs. We also show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds.
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order proximity/adjacency matrix of the graph via computationally expensive matrix factorization techniques. These approaches typically require significant resources for the learning process and rely on multiple parameters, which limits their applicability in practice. Moreover, most of the existing graph embedding techniques operate effectively in one specific metric space only (e.g., the one produced with cosine similarity), do not preserve higher-order structural features of the input graph and cannot automatically determine a meaningful number of embedding dimensions. Typically, the produced embeddings are not easily interpretable, which complicates further analyses and limits their applicability. To address these issues, we propose DAOR, a highly efficient and parameter-free graph embedding technique producing metric space-robust, compact and interpretable embeddings without any manual tuning. Compared to a dozen state-of-the-art graph embedding algorithms, DAOR yields competitive results on both node classification (which benefits form high-order proximity) and link prediction (which relies on low-order proximity mostly). Unlike existing techniques, however, DAOR does not require any parameter tuning and improves the embeddings generation speed by several orders of magnitude. Our approach has hence the ambition to greatly simplify and speed up data analysis tasks involving graph representation learning.
Multi-label image and video classification are fundamental yet challenging tasks in computer vision. The main challenges lie in capturing spatial or temporal dependencies between labels and discovering the locations of discriminative features for each class. In order to overcome these challenges, we propose to use cross-modality attention with semantic graph embedding for multi label classification. Based on the constructed label graph, we propose an adjacency-based similarity graph embedding method to learn semantic label embeddings, which explicitly exploit label relationships. Then our novel cross-modality attention maps are generated with the guidance of learned label embeddings. Experiments on two multi-label image classification datasets (MS-COCO and NUS-WIDE) show our method outperforms other existing state-of-the-arts. In addition, we validate our method on a large multi-label video classification dataset (YouTube-8M Segments) and the evaluation results demonstrate the generalization capability of our method.
Hashing techniques, also known as binary code learning, have recently gained increasing attention in large-scale data analysis and storage. Generally, most existing hash clustering methods are single-view ones, which lack complete structure or complementary information from multiple views. For cluster tasks, abundant prior researches mainly focus on learning discrete hash code while few works take original data structure into consideration. To address these problems, we propose a novel binary code algorithm for clustering, which adopts graph embedding to preserve the original data structure, called (Graph-based Multi-view Binary Learning) GMBL in this paper. GMBL mainly focuses on encoding the information of multiple views into a compact binary code, which explores complementary information from multiple views. In particular, in order to maintain the graph-based structure of the original data, we adopt a Laplacian matrix to preserve the local linear relationship of the data and map it to the Hamming space. Considering different views have distinctive contributions to the final clustering results, GMBL adopts a strategy of automatically assign weights for each view to better guide the clustering. Finally, An alternating iterative optimization method is adopted to optimize discrete binary codes directly instead of relaxing the binary constraint in two steps. Experiments on five public datasets demonstrate the superiority of our proposed method compared with previous approaches in terms of clustering performance.
Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and visualization. Most existing approaches represent graph nodes as point vectors in a low-dimensional embedding space, ignoring the uncertainty present in the real-world graphs. Furthermore, many real-world graphs are large-scale and rich in content (e.g. node attributes). In this work, we propose GLACE, a novel, scalable graph embedding method that preserves both graph structure and node attributes effectively and efficiently in an end-to-end manner. GLACE effectively models uncertainty through Gaussian embeddings, and supports inductive inference of new nodes based on their attributes. In our comprehensive experiments, we evaluate GLACE on real-world graphs, and the results demonstrate that GLACE significantly outperforms state-of-the-art embedding methods on multiple graph analysis tasks.
In this paper, we propose a new product knowledge graph (PKG) embedding approach for learning the intrinsic product relations as product knowledge for e-commerce. We define the key entities and summarize the pivotal product relations that are critical for general e-commerce applications including marketing, advertisement, search ranking and recommendation. We first provide a comprehensive comparison between PKG and ordinary knowledge graph (KG) and then illustrate why KG embedding methods are not suitable for PKG learning. We construct a self-attention-enhanced distributed representation learning model for learning PKG embeddings from raw customer activity data in an end-to-end fashion. We design an effective multi-task learning schema to fully leverage the multi-modal e-commerce data. The Poincare embedding is also employed to handle complex entity structures. We use a real-world dataset from grocery.walmart.com to evaluate the performances on knowledge completion, search ranking and recommendation. The proposed approach compares favourably to baselines in knowledge completion and downstream tasks.
Routing newly posted questions (a.k.a cold questions) to potential answerers with the suitable expertise in Community Question Answering sites (CQAs) is an important and challenging task. The existing methods either focus only on embedding the graph structural information and are less effective for newly posted questions, or adopt manually engineered feature vectors that are not as representative as the graph embedding methods. Therefore, we propose to address the challenge of leveraging heterogeneous graph and textual information for cold question routing by designing an end-to-end framework that jointly learns CQA node embeddings and finds best answerers for cold questions. We conducted extensive experiments to confirm the usefulness of incorporating the textual information from question tags and demonstrate that an end-2-end framework can achieve promising performances on routing newly posted questions asked by both existing users and newly registered users.