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Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don't match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover's Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach.[PUBLICATION ABSTRACT]

Graph analysis is becoming increasingly important due to the expressive power of graph models and the efficient algorithms available for processing them. Reinforcement Learning is one domain that could benefit from advancements in graph analysis, given that a learning agent may be integrated into an environment that can be represented as a graph. Nevertheless, the structural irregularity of graphs and the lack of prior labels make it difficult to integrate such a model into modern Reinforcement Learning frameworks that rely on artificial neural networks. Graph embedding enables the learning of low-dimensional vector representations that are more suited for machine learning algorithms, while retaining essential graph features. This paper presents a framework for evaluating graph embedding algorithms and their ability to preserve the structure and relevant features of graphs by means of an internal validation metric, without resorting to subsequent tasks that require labels for training. Based on this framework, three defined algorithms that meet the necessary requirements for solving a specific problem of Reinforcement Learning in graphs are selected, analyzed, and compared. These algorithms are Graph2Vec, GL2Vec, and Wavelet Characteristics, with the latter two demonstrating superior performance.

With the explosive growth of artificial intelligence (AI) and big data, it has become vitally important to organize and represent the enormous volume of knowledge appropriately. As graph data, knowledge graphs accumulate and convey knowledge of the real world. It has been well-recognized that knowledge graphs effectively represent complex information; hence, they rapidly gain the attention of academia and industry in recent years. Thus to develop a deeper understanding of knowledge graphs, this paper presents a systematic overview of this field. Specifically, we focus on the opportunities and challenges of knowledge graphs. We first review the opportunities of knowledge graphs in terms of two aspects: (1) AI systems built upon knowledge graphs; (2) potential application fields of knowledge graphs. Then, we thoroughly discuss severe technical challenges in this field, such as knowledge graph embeddings, knowledge acquisition, knowledge graph completion, knowledge fusion, and knowledge reasoning. We expect that this survey will shed new light on future research and the development of knowledge graphs.

Extracting hierarchical structure in graph data is becoming an important problem in fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods in non-Euclidean spaces, such as Poincaré embedding and Lorentz embedding, and it is now possible to learn efficient embedding by taking advantage of the structure of these spaces. In this study, we propose embedding into another type of metric space called a metric cone by learning an only one-dimensional coordinate variable added to the original vector space or a pre-trained embedding space. This allows for the extraction of hierarchical information while maintaining the properties of the pre-trained embedding. The metric cone is a one-dimensional extension of the original metric space and has the advantage that the curvature of the space can be easily adjusted by a parameter even when the coordinates of the original space are fixed. Through an extensive empirical evaluation we have corroborated the effectiveness of the proposed cone embedding model. In the case of randomly generated trees, cone embedding demonstrated superior performance in extracting hierarchical structures compared to existing techniques, particularly in high-dimensional settings. For WordNet embeddings, cone embedding exhibited a noteworthy correlation between the extracted hierarchical structures and human evaluation outcomes.

Knowledge graphs (KGs) have been widely used in the field of artificial intelligence, such as in information retrieval, natural language processing, recommendation systems, etc. However, the open nature of KGs often implies that they are incomplete, having self-defects. This creates the need to build a more complete knowledge graph for enhancing the practical utilization of KGs. Link prediction is a fundamental task in knowledge graph completion that utilizes existing relations to infer new relations so as to build a more complete knowledge graph. Numerous methods have been proposed to perform the link-prediction task based on various representation techniques. Among them, KG-embedding models have significantly advanced the state of the art in the past few years. In this paper, we provide a comprehensive survey on KG-embedding models for link prediction in knowledge graphs. We first provide a theoretical analysis and comparison of existing methods proposed to date for generating KG embedding. Then, we investigate several representative models that are classified into five categories. Finally, we conducted experiments on two benchmark datasets to report comprehensive findings and provide some new insights into the strengths and weaknesses of existing models.

Graph Neural Networks (GNNs) have achieved excellent performance of graph representation learning and attracted plenty of attentions in recent years. Most of GNNs aim to learn embedding vectors of the homogeneous graph which only contains single type of nodes and edges. However, the entities and their interactions in real world always have multiple types and naturally form the heterogeneous graph with rich structural and semantic information. As a result of this, it is beneficial to advance heterogeneous graph representation learning that can effectively promote the performance of complex network analysis. Existing survey papers of heterogeneous graph representation learning summarize all possible embedding techniques for graphs and make insufficient analysis for deep neural network models. To tackle this issue, in this paper, we systematically summarize and analyze existing heterogeneous graph neural networks (HGNNs) and categorize them based on their neural network architecture. Meanwhile, we collect commonly used heterogeneous graph datasets and summarize their statistical information. In addition, we compare the performances between HGNNs and shallow embedding models to show the powerful feature learning ability of HGNNs. Finally, we conclude the application scenarios of HGNNs and some possible future research directions. We hope that this paper can provide a useful framework for researchers who interested in HGNNs.

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA

Translation-based knowledge graph embeddings learn vector representations of entities and relations by treating relations as translation operators over the entities in an embedding space. Since the translation is represented through a score function, translation-based embeddings are trained in general by minimizing a margin-based ranking loss, which assigns a low score to positive triples and a high score to negative triples. However, this type of embedding suffers from slow convergence and poor local optima because the loss adopts only one pair of a positive and a negative triple at a single update of learning parameters. Therefore, this paper proposes the N-pair translation loss that considers multiple negative triples at one update. The N-pair translation loss employs multiple negative triples as well as one positive triple and allows the positive triple to be compared against the multiple negative triples at each parameter update. As a result, it becomes possible to obtain better vector representations rapidly. The experimental results on link prediction prove that the proposed loss helps to quickly converge toward good optima at the early stage of training.

High penetration of Android applications along with their malicious variants requires efficient and effective malware detection methods to build mobile platform security. API call sequence derived from API call graph structure can be used to model application behavior accurately. Behaviors are extracted by following the API call graph, its branching, and order of calls. But identification of similarities in graphs and graph matching algorithms for classification is slow, complicated to be adopted to a new domain, and their results may be inaccurate. In this study, the authors use the API call graph as a graph representation of all possible execution paths that a malware can track during its runtime. The embedding of API call graphs transformed into a low dimension numeric vector feature set is introduced to the deep neural network. Then, similarity detection for each binary function is trained and tested effectively. This study is also focused on maximizing the performance of the network by evaluating different embedding algorithms and tuning various network configuration parameters to assure the best combination of the hyper-parameters and to reach at the highest statistical metric value. Experimental results show that the presented malware classification is reached at 98.86% level in accuracy, 98.65% in F -measure, 98.47% in recall and 98.84% in precision, respectively.

Graphs are data structures that effectively represent relational data in the real world. Graph representation learning is a significant task since it could facilitate various downstream tasks, such as node classification, link prediction, etc. Graph representation learning aims to map graph entities to low-dimensional vectors while preserving graph structure and entity relationships. Over the decades, many models have been proposed for graph representation learning. This paper aims to show a comprehensive picture of graph representation learning models, including traditional and state-of-the-art models on various graphs in different geometric spaces. First, we begin with five types of graph embedding models: graph kernels, matrix factorization models, shallow models, deep-learning models, and non-Euclidean models. In addition, we also discuss graph transformer models and Gaussian embedding models. Second, we present practical applications of graph embedding models, from constructing graphs for specific domains to applying models to solve tasks. Finally, we discuss challenges for existing models and future research directions in detail. As a result, this paper provides a structured overview of the diversity of graph embedding models.