A weighted directed network (WDN) is a directed graph in which each edge is associated to a unique value called weight. These networks are very suitable for modeling real-world social networks in which there is an assessment of one vertex toward other vertices. One of the main problems studied in this paper is prediction of edge weights in such networks. We introduce, for the first time, a metric geometry approach to studying edge weight prediction in WDNs. We modify a usual notion of WDNs, and introduce a new type of WDNs which we coin the term \textit{almost-weighted directed networks} (AWDNs). AWDNs can capture the weight information of a network from a given training set. We then construct a class of metrics (or distances) for AWDNs which equips such networks with a metric space structure. Using the metric geometry structure of AWDNs, we propose modified $k$ nearest neighbors (kNN) methods and modified support-vector machine (SVM) methods which will then be used to predict edge weights in AWDNs. In many real-world datasets, in addition to edge weights, one can also associate weights to vertices which capture information of vertices; association of weights to vertices especially plays an important role in graph embedding problems. Adopting a similar approach, we introduce two new types of directed networks in which weights are associated to either a subset of origin vertices or a subset of terminal vertices . We, for the first time, construct novel classes of metrics on such networks, and based on these new metrics propose modified $k$NN and SVM methods for predicting weights of origins and terminals in these networks. We provide experimental results on several real-world datasets, using our geometric methodologies.
Static knowledge graph (SKG) embedding (SKGE) has been studied intensively in the past years. Recently, temporal knowledge graph (TKG) embedding (TKGE) has emerged. In this paper, we propose a Recursive Temporal Fact Embedding (RTFE) framework to transplant SKGE models to TKGs and to enhance the performance of existing TKGE models for TKG completion. Different from previous work which ignores the continuity of states of TKG in time evolution, we treat the sequence of graphs as a Markov chain, which transitions from the previous state to the next state. RTFE takes the SKGE to initialize the embeddings of TKG. Then it recursively tracks the state transition of TKG by passing updated parameters/features between timestamps. Specifically, at each timestamp, we approximate the state transition as the gradient update process. Since RTFE learns each timestamp recursively, it can naturally transit to future timestamps. Experiments on five TKG datasets show the effectiveness of RTFE.
We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure and neighborhood proximity in a single representation. The key idea is to transform the given graph into one whose weights measure the centrality of an edge by the fraction of the number of shortest paths that pass through that edge, and employ its spectral proprieties in the representation. Testing the resulting graph network representation shows significant improvement over the sate of the art in data analysis tasks including social networks and material science. We also test our method on node classification from the human-SARS CoV-2 protein-protein interactome.
Conventional Knowledge Graph Completion (KGC) assumes that all test entities appear during training. However, in real-world scenarios, Knowledge Graphs (KG) evolve fast with out-of-knowledge-graph (OOKG) entities added frequently, and we need to represent these entities efficiently. Most existing Knowledge Graph Embedding (KGE) methods cannot represent OOKG entities without costly retraining on the whole KG. To enhance efficiency, we propose a simple and effective method that inductively represents OOKG entities by their optimal estimation under translational assumptions. Given pretrained embeddings of the in-knowledge-graph (IKG) entities, our method needs no additional learning. Experimental results show that our method outperforms the state-of-the-art methods with higher efficiency on two KGC tasks with OOKG entities.
Recent advances in Knowledge Graph Embedding (KGE) allow for representing entities and relations in continuous vector spaces. Some traditional KGE models leveraging additional type information can improve the representation of entities which however totally rely on the explicit types or neglect the diverse type representations specific to various relations. Besides, none of the existing methods is capable of inferring all the relation patterns of symmetry, inversion and composition as well as the complex properties of 1-N, N-1 and N-N relations, simultaneously. To explore the type information for any KG, we develop a novel KGE framework with Automated Entity TypE Representation (AutoETER), which learns the latent type embedding of each entity by regarding each relation as a translation operation between the types of two entities with a relation-aware projection mechanism. Particularly, our designed automated type representation learning mechanism is a pluggable module which can be easily incorporated with any KGE model. Besides, our approach could model and infer all the relation patterns and complex relations. Experiments on four datasets demonstrate the superior performance of our model compared to state-of-the-art baselines on link prediction tasks, and the visualization of type clustering provides clearly the explanation of type embeddings and verifies the effectiveness of our model.
Graph embedding is a powerful method to represent graph neurological data (e.g., brain connectomes) in a low dimensional space for brain connectivity mapping, prediction and classification. However, existing embedding algorithms have two major limitations. First, they primarily focus on preserving one-to-one topological relationships between nodes (i.e., regions of interest (ROIs) in a connectome), but they have mostly ignored many-to-many relationships (i.e., set to set), which can be captured using a hyperconnectome structure. Second, existing graph embedding techniques cannot be easily adapted to multi-view graph data with heterogeneous distributions. In this paper, while cross-pollinating adversarial deep learning with hypergraph theory, we aim to jointly learn deep latent embeddings of subject0specific multi-view brain graphs to eventually disentangle different brain states. First, we propose a new simple strategy to build a hyperconnectome for each brain view based on nearest neighbour algorithm to preserve the connectivities across pairs of ROIs. Second, we design a hyperconnectome autoencoder (HCAE) framework which operates directly on the multi-view hyperconnectomes based on hypergraph convolutional layers to better capture the many-to-many relationships between brain regions (i.e., nodes). For each subject, we further regularize the hypergraph autoencoding by adversarial regularization to align the distribution of the learned hyperconnectome embeddings with that of the input hyperconnectomes. We formalize our hyperconnectome embedding within a geometric deep learning framework to optimize for a given subject, thereby designing an individual-based learning framework. Our experiments showed that the learned embeddings by HCAE yield to better results for brain state classification compared with other deep graph embedding methods methods.
Wikipedia is edited by volunteer editors around the world. Considering the large amount of existing content (e.g. over 5M articles in English Wikipedia), deciding what to edit next can be difficult, both for experienced users that usually have a huge backlog of articles to prioritize, as well as for newcomers who that might need guidance in selecting the next article to contribute. Therefore, helping editors to find relevant articles should improve their performance and help in the retention of new editors. In this paper, we address the problem of recommending relevant articles to editors. To do this, we develop a scalable system on top of Graph Convolutional Networks and Doc2Vec, learning how to represent Wikipedia articles and deliver personalized recommendations for editors. We test our model on editors' histories, predicting their most recent edits based on their prior edits. We outperform competitive implicit-feedback collaborative-filtering methods such as WMRF based on ALS, as well as a traditional IR-method such as content-based filtering based on BM25. All of the data used on this paper is publicly available, including graph embeddings for Wikipedia articles, and we release our code to support replication of our experiments. Moreover, we contribute with a scalable implementation of a state-of-art graph embedding algorithm as current ones cannot efficiently handle the sheer size of the Wikipedia graph.
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG they are brittle and mining ones that infer facts beyond the known KG is challenging. Probabilistic embedding methods are effective in capturing global soft statistical tendencies and reasoning with them is computationally efficient. While embedding representations learned from rich training data are expressive, incompleteness and sparsity in real-world KGs can impact their effectiveness. We aim to leverage the complementary properties of both methods to develop a hybrid model that learns both high-quality rules and embeddings simultaneously. Our method uses a cross feedback paradigm wherein, an embedding model is used to guide the search of a rule mining system to mine rules and infer new facts. These new facts are sampled and further used to refine the embedding model. Experiments on multiple benchmark datasets show the effectiveness of our method over other competitive standalone and hybrid baselines. We also show its efficacy in a sparse KG setting and finally explore the connection with negative sampling.
A graph embedding algorithm embeds a graph into a low-dimensional space such that the embedding preserves the inherent properties of the graph. While graph embedding is fundamentally related to graph visualization, prior work did not exploit this connection explicitly. We develop Force2Vec that uses force-directed graph layout models in a graph embedding setting with an aim to excel in both machine learning (ML) and visualization tasks. We make Force2Vec highly parallel by mapping its core computations to linear algebra and utilizing multiple levels of parallelism available in modern processors. The resultant algorithm is an order of magnitude faster than existing methods (43x faster than DeepWalk, on average) and can generate embeddings from graphs with billions of edges in a few hours. In comparison to existing methods, Force2Vec is better in graph visualization and performs comparably or better in ML tasks such as link prediction, node classification, and clustering. Source code is available at https://github.com/HipGraph/Force2Vec.
Pedestrian trajectory prediction is a critical to avoid autonomous driving collision. But this prediction is a challenging problem due to social forces and cluttered scenes. Such human-human and human-space interactions lead to many socially plausible trajectories. In this paper, we propose a novel LSTM-based algorithm. We tackle the problem by considering the static scene and pedestrian which combine the Graph Convolutional Networks and Temporal Convolutional Networks to extract features from pedestrians. Each pedestrian in the scene is regarded as a node, and we can obtain the relationship between each node and its neighborhoods by graph embedding. It is LSTM that encode the relationship so that our model predicts nodes trajectories in crowd scenarios simultaneously. To effectively predict multiple possible future trajectories, we further introduce Spatio-Temporal Convolutional Block to make the network flexible. Experimental results on two public datasets, i.e. ETH and UCY, demonstrate the effectiveness of our proposed ST-Block and we achieve state-of-the-art approaches in human trajectory prediction.
Knowledge graph embedding approaches represent nodes and edges of graphs as mathematical vectors. Current approaches focus on embedding complete knowledge graphs, i.e. all nodes and edges. This leads to very high computational requirements on large graphs such as DBpedia or Wikidata. However, for most downstream application scenarios, only a small subset of concepts is of actual interest. In this paper, we present RDF2Vec Light, a lightweight embedding approach based on RDF2Vec which generates vectors for only a subset of entities. To that end, RDF2Vec Light only traverses and processes a subgraph of the knowledge graph. Our method allows the application of embeddings of very large knowledge graphs in scenarios where such embeddings were not possible before due to a significantly lower runtime and significantly reduced hardware requirements.
Knowledge Graph Embedding (KGE) is a popular method for KG reasoning and training KGEs with higher dimension are usually preferred since they have better reasoning capability. However, high-dimensional KGEs pose huge challenges to storage and computing resources and are not suitable for resource-limited or time-constrained applications, for which faster and cheaper reasoning is necessary. To address this problem, we propose DualDE, a knowledge distillation method to build low-dimensional student KGE from pre-trained high-dimensional teacher KGE. DualDE considers the dual-influence between the teacher and the student. In DualDE, we propose a soft label evaluation mechanism to adaptively assign different soft label and hard label weights to different triples, and a two-stage distillation approach to improve the student's acceptance of the teacher. Our DualDE is general enough to be applied to various KGEs. Experimental results show that our method can successfully reduce the embedding parameters of a high-dimensional KGE by 7 times - 15 times and increase the inference speed by 2 times - 6 times while retaining a high performance. We also experimentally prove the effectiveness of our soft label evaluation mechanism and two-stage distillation approach via ablation study.
Extracting structured knowledge from texts has traditionally been used for knowledge base generation. However, other sources of information, such as images can be leveraged into this process to build more complete and richer knowledge bases. Structured semantic representation of the content of an image and knowledge graph embeddings can provide a unique representation of semantic relationships between image entities. Linking known entities in knowledge graphs and learning open-world images using language models has attracted lots of interest over the years. In this paper, we propose a shared learning approach to learn semantic attributes of images by combining a knowledge graph embedding model with the recognized attributes of images. The proposed model premises to help us understand the semantic relationship between the entities of an image and implicitly provide a link for the extracted entities through a knowledge graph embedding model. Under the limitation of using a custom user-defined knowledge base with limited data, the proposed model presents significant accuracy and provides a new alternative to the earlier approaches. The proposed approach is a step towards bridging the gap between frameworks which learn from large amounts of data and frameworks which use a limited set of predicates to infer new knowledge.
Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well, because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against that of traditional community detection algorithms. We find that the performance is comparable, if the parameters of the embedding techniques are suitably chosen. However, the optimal parameter set varies with the specific features of the benchmark graphs, like their size, whereas popular community detection algorithms do not require any parameter. So it is not possible to indicate beforehand good parameter sets for the analysis of real networks. This finding, along with the high computational cost of embedding a network and grouping the points, suggests that, for community detection, current embedding techniques do not represent an improvement over network clustering algorithms.
Scalar coupling constant (SCC) plays a key role in the analysis of three-dimensional structure of organic matter, however, the traditional SCC prediction using quantum mechanical calculations is very time-consuming. To calculate SCC efficiently and accurately, we proposed a graph embedding local self-attention encoder (GELAE) model, in which, a novel invariant structure representation of the coupling system in terms of bond length, bond angle and dihedral angle was presented firstly, and then a local self-attention module embedded with the adjacent matrix of a graph was designed to extract effectively the features of coupling systems, finally, with a modified classification loss function, the SCC was predicted. To validate the superiority of the proposed method, we conducted a series of comparison experiments using different structure representations, different attention modules, and different losses. The experimental results demonstrate that, compared to the traditional chemical bond structure representations, the rotation and translation invariant structure representations proposed in this work can improve the SCC prediction accuracy; with the graph embedded local self-attention, the mean absolute error (MAE) of the prediction model in the validation set decreases from 0.1603 Hz to 0.1067 Hz; using the classification based loss function instead of the scaled regression loss, the MAE of the predicted SCC can be decreased to 0.0963 HZ, which is close to the quantum chemistry standard on CHAMPS dataset.
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many areas of research and industry. However, the irregular structure of graph data constitutes an obstacle for running ML tasks on graphs such as link prediction, node classification, and anomaly detection. Graph embedding is a compute-intensive process of representing graphs as a set of vectors in a d-dimensional space, which in turn makes it amenable to ML tasks. Many approaches have been proposed in the literature to improve the performance of graph embedding, e.g., using distributed algorithms, accelerators, and pre-processing techniques. Graph coarsening, which can be considered a pre-processing step, is a structural approximation of a given, large graph with a smaller one. As the literature suggests, the cost of embedding significantly decreases when coarsening is employed. In this work, we thoroughly analyze the impact of the coarsening quality on the embedding performance both in terms of speed and accuracy. Our experiments with a state-of-the-art, fast graph embedding tool show that there is an interplay between the coarsening decisions taken and the embedding quality.
TorchKGE is a Python module for knowledge graph (KG) embedding relying solely on PyTorch. This package provides researchers and engineers with a clean and efficient API to design and test new models. It features a KG data structure, simple model interfaces and modules for negative sampling and model evaluation. Its main strength is a very fast evaluation module for the link prediction task, a central application of KG embedding. Various KG embedding models are also already implemented. Special attention has been paid to code efficiency and simplicity, documentation and API consistency. It is distributed using PyPI under BSD license. Source code and pointers to documentation and deployment can be found at https://github.com/torchkge-team/torchkge.
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty. Thus, learning directly from raw data can be misleading and can negatively impact the accuracy. In this paper, we propose to model artifacts in training data using probability distributions; each data point is represented by a Gaussian distribution centered at the original data point and having a variance modeling its uncertainty. We reformulate the Graph Embedding framework to make it suitable for learning from distributions and we study as special cases the Linear Discriminant Analysis and the Marginal Fisher Analysis techniques. Furthermore, we propose two schemes for modeling data uncertainty based on pair-wise distances in an unsupervised and a supervised contexts.
Link prediction in dynamic graphs (LPDG) is an important research problem that has diverse applications such as online recommendations, studies on disease contagion, organizational studies, etc. Various LPDG methods based on graph embedding and graph neural networks have been recently proposed and achieved state-of-the-art performance. In this paper, we study the vulnerability of LPDG methods and propose the first practical black-box evasion attack. Specifically, given a trained LPDG model, our attack aims to perturb the graph structure, without knowing to model parameters, model architecture, etc., such that the LPDG model makes as many wrong predicted links as possible. We design our attack based on a stochastic policy-based RL algorithm. Moreover, we evaluate our attack on three real-world graph datasets from different application domains. Experimental results show that our attack is both effective and efficient.
We consider the problem of learning efficient and inductive graph convolutional networks for text classification with a large number of examples and features. Existing state-of-the-art graph embedding based methods such as predictive text embedding (PTE) and TextGCN have shortcomings in terms of predictive performance, scalability and inductive capability. To address these limitations, we propose a heterogeneous graph convolutional network (HeteGCN) modeling approach that unites the best aspects of PTE and TextGCN together. The main idea is to learn feature embeddings and derive document embeddings using a HeteGCN architecture with different graphs used across layers. We simplify TextGCN by dissecting into several HeteGCN models which (a) helps to study the usefulness of individual models and (b) offers flexibility in fusing learned embeddings from different models. In effect, the number of model parameters is reduced significantly, enabling faster training and improving performance in small labeled training set scenario. Our detailed experimental studies demonstrate the efficacy of the proposed approach.