A brain can detect outlier just by using only normal samples. Similarly, one-class classification (OCC) also uses only normal samples to train the model and trained model can be used for outlier detection. In this paper, a multi-layer architecture for OCC is proposed by stacking various Graph-Embedded Kernel Ridge Regression (KRR) based Auto-Encoders in a hierarchical fashion. These Auto-Encoders are formulated under two types of Graph-Embedding, namely, local and global variance-based embedding. This Graph-Embedding explores the relationship between samples and multi-layers of Auto-Encoder project the input features into new feature space. The last layer of this proposed architecture is Graph-Embedded regression-based one-class classifier. The Auto-Encoders use an unsupervised approach of learning and the final layer uses semi-supervised (trained by only positive samples and obtained closed-form solution) approach to learning. The proposed method is experimentally evaluated on 21 publicly available benchmark datasets. Experimental results verify the effectiveness of the proposed one-class classifiers over 11 existing state-of-the-art kernel-based one-class classifiers. Friedman test is also performed to verify the statistical significance of the claim of the superiority of the proposed one-class classifiers over the existing state-of-the-art methods. By using two types of Graph-Embedding, 4 variants of Graph-Embedded multi-layer KRR-based one-class classifier has been presented in this paper. All 4 variants performed better than the existing one-class classifiers in terms of various discussed criteria in this paper. Hence, it can be a viable alternative for OCC task. In the future, various other types of Auto-Encoders can be explored within proposed architecture.
Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a social network, or a protein in a protein-protein interaction network. In this work, we consider a more challenging but practically useful setting, in which a node itself is a graph instance. This leads to a hierarchical graph perspective which arises in many domains such as social network, biological network and document collection. For example, in a social network, a group of people with shared interests forms a user group, whereas a number of user groups are interconnected via interactions or common members. We study the node classification problem in the hierarchical graph where a `node' is a graph instance, e.g., a user group in the above example. As labels are usually limited in real-world data, we design two novel semi-supervised solutions named \underline{SE}mi-supervised gr\underline{A}ph c\underline{L}assification via \underline{C}autious/\underline{A}ctive \underline{I}teration (or SEAL-C/AI in short). SEAL-C/AI adopt an iterative framework that takes turns to build or update two classifiers, one working at the graph instance level and the other at the hierarchical graph level. To simplify the representation of the hierarchical graph, we propose a novel supervised, self-attentive graph embedding method called SAGE, which embeds graph instances of arbitrary size into fixed-length vectors. Through experiments on synthetic data and Tencent QQ group data, we demonstrate that SEAL-C/AI not only outperform competing methods by a significant margin in terms of accuracy/Macro-F1, but also generate meaningful interpretations of the learned representations.
Representation learning on graphs has emerged as a powerful mechanism to automate feature vector generation for downstream machine learning tasks. The advances in representation on graphs have centered on both homogeneous and heterogeneous graphs, where the latter presenting the challenges associated with multi-typed nodes and/or edges. In this paper, we consider the additional challenge of evolving graphs. We ask the question of whether the advances in representation learning for static graphs can be leveraged for dynamic graphs and how? It is important to be able to incorporate those advances to maximize the utility and generalization of methods. To that end, we propose the Framework for Incremental Learning of Dynamic Networks Embedding (FILDNE), which can utilize any existing static representation learning method for learning node embeddings, while keeping the computational costs low. FILDNE integrates the feature vectors computed using the standard methods over different timesteps into a single representation by developing a convex combination function and alignment mechanism. Experimental results on several downstream tasks, over seven real-world data sets, show that FILDNE is able to reduce memory and computational time costs while providing competitive quality measure gains with respect to the contemporary methods for representation learning on dynamic graphs.
Knowledge graphs have evolved rapidly in recent years and their usefulness has been demonstrated in many artificial intelligence tasks. However, knowledge graphs often have lots of missing facts. To solve this problem, many knowledge graph embedding models have been developed to populate knowledge graphs and these have shown outstanding performance. However, knowledge graph embedding models are so-called black boxes, and the user does not know how the information in a knowledge graph is processed and the models can be difficult to interpret. In this paper, we utilize graph patterns in a knowledge graph to overcome such problems. Our proposed model, the {\it graph pattern entity ranking model} (GRank), constructs an entity ranking system for each graph pattern and evaluates them using a ranking measure. By doing so, we can find graph patterns which are useful for predicting facts. Then, we perform link prediction tasks on standard datasets to evaluate our GRank method. We show that our approach outperforms other state-of-the-art approaches such as ComplEx and TorusE for standard metrics such as HITS@{\it n} and MRR. Moreover, our model is easily interpretable because the output facts are described by graph patterns.
Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classification task: (1)when only the largest sub-graph structure ($k$-hop neighbor) is used for neighborhood aggregation, a large amount of early-stage information is lost during the graph convolution step; (2) simple average/sum pooling or max pooling utilized, which loses the characteristics of each node and the topology between nodes. In this paper, we propose a novel framework called, dual attention graph convolutional networks (DAGCN) to address these problems. DAGCN automatically learns the importance of neighbors at different hops using a novel attention graph convolution layer, and then employs a second attention component, a self-attention pooling layer, to generalize the graph representation from the various aspects of a matrix graph embedding. The dual attention network is trained in an end-to-end manner for the graph classification task. We compare our model with state-of-the-art graph kernels and other deep learning methods. The experimental results show that our framework not only outperforms other baselines but also achieves a better rate of convergence.
We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general framework that provides a novel means to performing graph-level embedding in a completely unsupervised and inductive manner. The learned neural network can be considered as a function that receives any graph as input, either seen or unseen in the training set, and transforms it into an embedding. A novel graph-level embedding generation mechanism called Multi-Scale Node Attention (MSNA), is proposed. Experiments on five real graph datasets show that UGRAPHEMB achieves competitive accuracy in the tasks of graph classification, similarity ranking, and graph visualization.
With the advantage of low storage cost and high efficiency, hashing learning has received much attention in the domain of Big Data. In this paper, we propose a novel unsupervised hashing learning method to cope with this open problem to directly preserve the manifold structure by hashing. To address this problem, both the semantic correlation in textual space and the locally geometric structure in the visual space are explored simultaneously in our framework. Besides, the `2;1-norm constraint is imposed on the projection matrices to learn the discriminative hash function for each modality. Extensive experiments are performed to evaluate the proposed method on the three publicly available datasets and the experimental results show that our method can achieve superior performance over the state-of-the-art methods.
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.
Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.
Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph embedding methods, such as Canonical decomposition/Parallel factorization (CP), DistMult, and ComplEx, have been proposed to address this issue. These methods represent entities and relations as embedding vectors in semantic space and predict the links between them. The embedding vectors themselves contain rich semantic information and can be used in other applications such as data analysis. However, mechanisms in these models and the embedding vectors themselves vary greatly, making it difficult to understand and compare them. Given this lack of understanding, we risk using them ineffectively or incorrectly, particularly for complicated models, such as CP, with two role-based embedding vectors, or the state-of-the-art ComplEx model, with complex-valued embedding vectors. In this paper, we propose a multi-embedding interaction mechanism as a new approach to uniting and generalizing these models. We derive them theoretically via this mechanism and provide empirical analyses and comparisons between them. We also propose a new multi-embedding model based on quaternion algebra and show that it achieves promising results using popular benchmarks. Source code is available on GitHub at https://github.com/tranhungnghiep/AnalyzeKGE.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
Graph embedding technics are studied with interest on public datasets, such as BlogCatalog, with the common practice of maximizing scoring on graph reconstruction, link prediction metrics etc. However, in the financial sector the important metrics are often more business related, for example fraud detection rates. With our privileged position of having large amount of real-world non-public P2P-lending social data, we aim to study empirically whether recent advances in graph embedding technics provide a useful signal for metrics more closely related to business interests, such as fraud detection rate.
Patent landscaping is a method used for searching related patents during a research and development (R&D) project. To avoid the risk of patent infringement and to follow current trends in technology, patent landscaping is a crucial task required during the early stages of an R&D project. As the process of patent landscaping requires advanced resources and can be tedious, the demand for automated patent landscaping has been gradually increasing. However, a shortage of well-defined benchmark datasets and comparable models makes it difficult to find related research studies. In this paper, we propose an automated patent landscaping model based on deep learning. To analyze the text of patents, the proposed model uses a modified transformer structure. To analyze the metadata of patents, we propose a graph embedding method that uses a diffusion graph called Diff2Vec. Furthermore, we introduce four benchmark datasets for comparing related research studies in patent landscaping. The datasets are produced by querying Google BigQuery, based on a search formula from a Korean patent attorney. The obtained results indicate that the proposed model and datasets can attain state-of-the-art performance, as compared with current patent landscaping models.
Knowledge graph embedding aims to learn distributed representations for entities and relations, and is proven to be effective in many applications. Crossover interactions --- bi-directional effects between entities and relations --- help select related information when predicting a new triple, but haven't been formally discussed before. In this paper, we propose CrossE, a novel knowledge graph embedding which explicitly simulates crossover interactions. It not only learns one general embedding for each entity and relation as most previous methods do, but also generates multiple triple specific embeddings for both of them, named interaction embeddings. We evaluate embeddings on typical link prediction tasks and find that CrossE achieves state-of-the-art results on complex and more challenging datasets. Furthermore, we evaluate embeddings from a new perspective --- giving explanations for predicted triples, which is important for real applications. In this work, an explanation for a triple is regarded as a reliable closed-path between the head and the tail entity. Compared to other baselines, we show experimentally that CrossE, benefiting from interaction embeddings, is more capable of generating reliable explanations to support its predictions.
Large scale knowledge graph embedding has attracted much attention from both academia and industry in the field of Artificial Intelligence. However, most existing methods concentrate solely on fact triples contained in the given knowledge graph. Inspired by the fact that logic rules can provide a flexible and declarative language for expressing rich background knowledge, it is natural to integrate logic rules into knowledge graph embedding, to transfer human knowledge to entity and relation embedding, and strengthen the learning process. In this paper, we propose a novel logic rule-enhanced method which can be easily integrated with any translation based knowledge graph embedding model, such as TransE . We first introduce a method to automatically mine the logic rules and corresponding confidences from the triples. And then, to put both triples and mined logic rules within the same semantic space, all triples in the knowledge graph are represented as first-order logic. Finally, we define several operations on the first-order logic and minimize a global loss over both of the mined logic rules and the transformed first-order logics. We conduct extensive experiments for link prediction and triple classification on three datasets: WN18, FB166, and FB15K. Experiments show that the rule-enhanced method can significantly improve the performance of several baselines. The highlight of our model is that the filtered Hits@1, which is a pivotal evaluation in the knowledge inference task, has a significant improvement (up to 700% improvement).
An implementation of "Binarized Attributed Network Embedding". Attributed network embedding enables joint representation learning of node links and attributes. Existing attributed network embedding models are designed in continuous Euclidean spaces which often introduce data redundancy and impose challenges to storage and computation costs. To this end, we present a Binarized Attributed Network Embedding model (BANE for short) to learn binary node representation. Specifically, we define a new Weisfeiler-Lehman proximity matrix to capture data dependence between node links and attributes by aggregating the information of node attributes and links from neighboring nodes to a given target node in a layer-wise manner. Based on the Weisfeiler-Lehman proximity matrix, we formulate a new Weisfiler-Lehman matrix factorization learning function under the binary node representation constraint. The learning problem is a mixed integer optimization and an efficient cyclic coordinate descent (CCD) algorithm is used as the solution. Node classification and link prediction experiments on real-world datasets show that the proposed BANE model outperforms the state-of-the-art network embedding methods.
In this work, we propose the first quantum Ans\"atze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.
Graph Convolutional Networks(GCNs) play a crucial role in graph learning tasks, however, learning graph embedding with few supervised signals is still a difficult problem. In this paper, we propose a novel training algorithm for Graph Convolutional Network, called Multi-Stage Self-Supervised(M3S) Training Algorithm, combined with self-supervised learning approach, focusing on improving the generalization performance of GCNs on graphs with few labeled nodes. Firstly, a Multi-Stage Training Framework is provided as the basis of M3S training method. Then we leverage DeepCluster technique, a popular form of self-supervised learning, and design corresponding aligning mechanism on the embedding space to refine the Multi-Stage Training Framework, resulting in M3S Training Algorithm. Finally, extensive experimental results verify the superior performance of our algorithm on graphs with few labeled nodes under different label rates compared with other state-of-the-art approaches.
We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction.
An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can be used for machine learning, similarity search, or similar tasks. We address the problem of finding vector space embeddings for theories in the Description Logic $\mathcal{EL}^{++}$ that are also models of the TBox. To find such embeddings, we define an optimization problem that characterizes the model-theoretic semantics of the operators in $\mathcal{EL}^{++}$ within $\Re^n$, thereby solving the problem of finding an interpretation function for an $\mathcal{EL}^{++}$ theory given a particular domain $\Delta$. Our approach is mainly relevant to large $\mathcal{EL}^{++}$ theories and knowledge bases such as the ontologies and knowledge graphs used in the life sciences. We demonstrate that our method can be used for improved prediction of protein--protein interactions when compared to semantic similarity measures or knowledge graph embedding