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About 10,000 papers for “graph embedding”

Graph Embedding

Shirui Pan · TIB Data Manager · 2024

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Graph Embedding

University Research Chair · Encyclopedia of Database Systems · 2009

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Graph Embedding via Graph Summarization

Jingyanning Yang, Jinguo You, Xiaorong Wan · IEEE Access · 2021

Graph representation learning aims to represent the structural and semantic information of graph objects as dense real value vectors in low dimensional space by machine learning. It is widely used in node classification, link prediction, and recommendation systems. However, directly computing the embeddings for original graphs is prohibitively inefficient, especially for large-scale graphs. To address this issue, we present the GSE (Graph Summarization Embedding) model, a more efficient model that computes the nodes’ embeddings based on graph summarization. Specifically, the model first searches for the minimum information entropy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> groups to transform the original graph into a hypergraph with higher-order structural features. Next, the summarization graph’s connection probabilities are used to determine the biased random walks on the hypergraph, which then generates the sequences of the super-nodes. Finally, the node sequences are fed into the skip-gram to generate the vectors of these nodes. Our proposed model improves the efficiency of graph embedding on big data graphs and effectively alleviates the local optimal problem caused by the random walks. Experimental results demonstrate that GSE outperforms main existing clustering baselines, such as K_Means Clustering, Affinity Propagation Clustering, Canopy Clustering, and ACP Clustering. Moreover, our model can be coupled with the main graph embedding methods and improves the Macro-F1 scores and Micro-F1 scores for classification tasks on a variety of real-world graph data.

Cited by 8Open access

Modulo graph embedding

Hyunchul Park, Kevin Fan, Manjunath Kudlur et al. · 2006

Coarse-grained reconfigurable architectures (CGRAs) present an appealing hardware platform by providing the potential for high computation throughput, scalability, low cost and energy efficiency. CGRAs consist of an array of function units and register files generally organized as a two dimensional grid. The most difficult challenge with deploying CGRAs is compiler scheduling technology that can map software implementations of compute intensive loops onto the array. Traditional schedulers are not suitable because they do not take into account the explicit routing of operand values that is necessary. In essence, the problem of binding operations to time slots and resources is extended to also include explicit routing of operands from producers to consumers. To tackle this problem, this paper introduces a software pipelining technique for mapping loop bodies onto CGRAs, referred to as modulo graph embedding. We leverage graph embedding from graph theory, which is used to draw graphs onto a target space. The loop body is essentially drawn onto the CGRA mesh, subject to modulo resource usage constraints. Modulo graph embedding is effective because it can take into account the communication structure of the loop body during mapping. On average, a compute utilization of 56-68% is achieved for a set of loop kernels across three 4x4 CGRA designs.

Cited by 86

Combinatorial Graph Embedding.

Richard A. DeMillo, Sarah Eisenstat, R.J. Lipton · 1980

Abstract : Let G, G' be directed graphs. A combinatorial embedding of G into G' is an identification of each x an element of V(G) with a set of vertices S a subset of V(G') such that each S is bounded in size by a constant independent of V(G) and each arc in G is carried into a directed path of length bounded by a constant independent of V(G). This concept has formed the basis for a number of theoretical studies and the papers collected here are representative of - with one major exception - the state-of-the-art with regard to graph embedding.

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Graph embedding algorithms

Gagarin, Andrei Vladimirovich · Mspace (University of Manitoba) · 2003

A topologi,cal surface,S can be obtained from the sphere by adding a number of handles and/or cross-caps.Any topological surface can be represented as a polygon whose sides are identified in pairs.The projectiue plane can be represented as a circular disk with opposite pairs of points on its boundary identified.The torus can be represented as a rectangle with opposite sides of its boundary identified.Given a graph G and a topological surface ^9, we ask whether it is possible to ''251.This was published in the 1930s.However efficient algorithms to rec- ognize if a graph is planar appeared much later.For example, the popular linear time planarity-testing algorithm by J. Hopcroft and R. Tarjan [19] was published only in 7974.The ori,entable (non-ori,entable) genus of a graph is the smallest orientable (non-orientable) genus of a surface in which the graph can be embedded.In general, the problem of finding the genus of a graph was proved to be l/P-complete by C. Thomassen [36].Recently, Kuratowski's characterization of planar graphs v/as generalized for non-orientable surfaces by D. Archdeacon and J.P. Huneke [2] and for orientable surfaces by R.Bodendiek and K. Wagner [3].In a series of papers on graph minors, N. Robertson and P. Seymour [35] generalized Kuratowski's result for an arbitrary surface.This implies that for a given surface the ques- tion of whether a graph is embeddable into the surface can be answered in polynomial time.Moreover, B. Mohar [29] claimed to develop a series of linear time algorithms to answer the question.Unfortunately, these linear time algorithms appear to be infeasible, and are more of theoretical interest than practical.The de- scriptions of [28], [21] and [29] are missing many of the details necessary for an implementation of them.It is not clear if the approach is correct and covers all the cases providing a linear time algorithm.However, as it is mentioned in [41], the description of 128] gives some insights into the problem.The only known efficient implemented algorithm is the O(n') projective planarity-checking algorithm by W. Myrvold and J. Roth [30].This thesis is focussed on devising linear time practical algorithms to determine if there exists an embedding of a graph in the projective plane and/or torus.These are the topological surfaces closest to the plane.Early algorithms for these surfaces described in [12] and [32] are known to be wrong (personal communication by W. Myrvold).Many known algorithms for the projective plane and torus (eg.[30], [28] and [21]) begin with a Kuratowski subgraph Ks or K,s in a graph, and try to extend an embedding of K5 or Ks,s to an embedding of the whole graph on the corresponding surface.For a graph G containing a K5-subdivision, this thesis presents new algorithms to reduce the projective planarity or toroidality testing of G to a constant number of planarity checks or to a K,s-subdivision in G.For a graph G containing a K3,3-subdivision, the thesis provides a new detailed algorithm to tell if G is projective planar.In summary, we have devised a ne'vr/ Iinear time algorithm to detect a projective planar graph and a linear time algorithm that either determines the toroidality of a graph or returns a K3,3-subdivision in it.Chapter 2 provides basic notation, definitions and results related to the prob- lem and algorithms.Chapter 3 describes the main ideas of the Hopcroft-Tarjan planarity algorithm.The ideas and concepts of the planarity algorithm are used in different forms for other algorithms in the thesis.Necessary conditions for a 2-cell embedding of a graph on the projective plane and torus are given in Chapter 4. Section 4.3 presents methods for transforming a planar embed- ding into a2-cell embedding on the projective plane and torus.The methods are another main contribution of the thesis.They are used in the software GroupsJGraphs [2a].In Chapter 5, we describe known implemented general algorithms for the pro- jective plane and torus from [30] and [31].These algorithms help us to better understand surfaces with respect to the problem and its practical solution.The projective planarity checking algorithm of W. Myrvold and J. Roth has O(n2) time complexity, whereas the toroidality checking algorithm is exponential in the worst case.We have completely characterized projective planar and toroidal embeddings of certain kinds of graphs containing a K5-subdivision and developed linear time algorithms to tell if the graphs are projective planar or toroidal.Structural results for graphs containing a subdivision of K5 are presented in Chapter 6.Given a non-planar graph G with a subdivision of Ks as a subgraph, we can either transform the K5-subdivision into a Ks,g-subdivision in G, or else we obtain a partition of the vertices of G\/(s into equivalence classes.As a result, '/e can reduce a projective planarity or toroidality algorithm to a small constant number of planarity checks as in [19], or to a graph G containing a Ks,s-subdivision.The corresponding new algorithms are described in Section 7.1 for the projective plane and in Chapter 9 for the torus.Our new algorithms are reasonable to implement.This approach significantly simplifies algorithms presented in [21], [28] and [30].We then need to consider only the embeddings on the given surface of a K3,3-subdivision, which are much less numerous and more symmetric than those of K5.Also our new linear time algorithm of Chapter 9 can be used to restrict the exponential algorithm of [31] to graphs containing a K3,3-subdivision.A description of our new linear time projective planarity algorithm is presented in Chapters 7 and 8.This algorithm is more efficient than the O(n2) time algorithm of [30] described in Section 5.1.Chapter 7 describes structural results and all possible cases to complete a Ks,s-subdivision to an embedding of a graph G in the projective plane.We consider a spanning subdivision of.K3p in the graph.A case of a non-spanning Ks,s-subdivision in G can be treated recursively by using the recursion ideas of the Hopcroft-Tarjan planarity algorithm.Recent results of [11] suggest an efficient method to compute the orientable genus for a graph embedded in the projective plane.Our projective planarity algorithm can be used as a preliminary step to use the approach of [11].A graph embedding can be used to design a VLSI layout.Given a VLSI to design, we can represent its elements and wire connections by vertices and edges of a graph.Since connections between elements should not cross, v/e are interested in a drawing of the graph without edge crossing.This provides a practical motivation to obtain a graph embedding with particular properties.Chapter 2 Graphs and Surfaces: Basic Notation and ResultsBasic graph-theoretic terminology in this thesis follows Bondy and Murty [4] and Diestel [8].A graph G : (V, E) is undi,rected 1f. the edges of G are un- ordered pairs of vertices and G is si,mple if there are no multiple edges or loops.A graph G : (V, E) is 2-connected if for any two vertices)'tLiu e V, there are two internally disjoint paths in G with endpoints z and a.In other words, any two vertices u,u e V are on a cycle in G.In this thesis we consider the graph embedding problem for 2-connected, undirected, simple graphs.For graphs that are not 2-connected we can decide on their embedding in the plane, projective plane or torus by considering their maximal 2-connected subgraphs.Chapter 2 describes the polygon representation of the surfaces, defines an embedding of a graph and related things.Finally, the chapter describes basic results related to the graph embedding algorithms. 2.L Basic Notation and DefinitionsThe description of topological closed surfaces is taken from [13].The only topologically distinct (i.e.non-homeomorphic) types of.closed ori,entable sur- faces arc the sphere, the torus, and, in general, the generalized torus with p holes or the sphere with p handles (p:1,2,3,...).For closed non-ortentable surfaces, the only topologically distinct types are given by the sphere with q cross-caps (q : L,2,3,.. .).According to [13], any closed surface ^9 can be constructed from a curvilinear polygon homeomorphic to a circular disk by identifying sides in pairs.Each side from a pair is denoted by the same indexed symbol and is oriented on the polygon boundary.We use the superscript " * " to denote a clockwise orientation of a side, like a+, and the superscript " -" to denote a counter- clockwise orientation of a side, like -, on the polygon boundary.Also it can be proved that any surface ^9 can be decomposed into such a polygon.

Cited by 0Open access

Graph Embedding Methods for Graph Completion

Janchevski, Andrej · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2021

Knowledge graphs have recently attracted significant attention from both industry and academia in scenarios that require exploiting large-scale heterogeneous data collections. Knowledge graphs are a type of database where the general structure is a network of entities, their semantic types, properties, and relationships. They support reasoning over the integrated information as the main application. This process is very closely linked to solving the problems of link prediction and query answering for the knowledge graph. The most common approach in tackling these tasks is to compute suitable numeric representations for each graph element, called graph embeddings. In this work, we present an approach to constructing a model that generates meaningful graph representations while maintaining as significant scalability and prediction performance as possible. During preprocessing, network analysis techniques provide graph features, which are utilized by a novel graph embedding model that integrates local representations, obtained using standard and state-of-the-art techniques, into a global picture. Evaluation results show that the approach performs significantly well on the link prediction and query answering tasks on data from Swisscom, achieving accuracy of more than 90% and 50% respectively, reproducing results reported in related work. Certain experiments on academic data confirm the possibility for even further improvement through more focused research.

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Croppable Knowledge Graph Embedding

Association for Computational Linguistics 2025, Chen, Huajun, Chen, Mingyang et al. · Underline Science Inc. · 2025

Knowledge Graph Embedding (KGE) is a common approach for Knowledge Graphs (KGs) in AI tasks. Embedding dimensions depend on application scenarios. Requiring a new dimension means training a new KGE model from scratch, increasing cost and limiting efficiency and flexibility. In this work, we propose a novel KGE training framework MED. It allows one training to obtain a croppable KGE model for multiple scenarios with different dimensional needs. Sub-models of required dimensions can be directly cropped and used without extra training. In MED, we propose a mutual learning mechanism to improve the low-dimensional sub-models and make high-dimensional sub-models retain the low-dimensional sub-models' capacity, an evolutionary improvement mechanism to promote the high-dimensional sub-models to master the triple that the low-dimensional sub-models can not, and a dynamic loss weight to adaptively balance the multiple losses. Experiments on 4 KGE models across 4 standard KG completion datasets, 3 real-world scenarios using a large-scale KG, and extending MED to the BERT language model demonstrate its effectiveness, high efficiency, and flexible extensibility.

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Fuzzy Multilevel Graph Embedding

Muhammad Muzzamil Luqman, Jean-Yves Ramel, Josep Lladós et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2013

Cited by 3

Schematics for graph embedding.

Takuro Matsuta (21608505), Ryo Furue (11772699) · Figshare · 2025

Schematics showing (a) the spin configuration of a virtual annealing machine, (b) the spin configuration of the Hamiltonian (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0326303#pone.0326303.e129" target="_blank">Equation (26)</a>), and (c) how the Hamiltonian is embedded in the machine’s connectivity graph. The blue-colored qubits and are introduced to represent the graph topoglogy of (b). A penalty term will be added to the Hamiltonian to enforce the equality of and .

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Weighted Knowledge Graph Embedding

Zhao Zhang, Zhanpeng Guan, Fuwei Zhang et al. · 2023

Knowledge graph embedding (KGE) aims to project both entities and relations in a knowledge graph (KG) into low-dimensional vectors. Indeed, existing KGs suffer from the data imbalance issue, i.e., entities and relations conform to a long-tail distribution, only a small portion of entities and relations occur frequently, while the vast majority of entities and relations only have a few training samples. Existing KGE methods assign equal weights to each entity and relation during the training process. Under this setting, long-tail entities and relations are not fully trained during training, leading to unreliable representations. In this paper, we propose WeightE, which attends differentially to different entities and relations. Specifically, WeightE is able to endow lower weights to frequent entities and relations, and higher weights to infrequent ones. In such manner, WeightE is capable of increasing the weights of long-tail entities and relations, and learning better representations for them. In particular, WeightE tailors bilevel optimization for the KGE task, where the inner level aims to learn reliable entity and relation embeddings, and the outer level attempts to assign appropriate weights for each entity and relation. Moreover, it is worth noting that our technique of applying weights to different entities and relations is general and flexible, which can be applied to a number of existing KGE models. Finally, we extensively validate the superiority of WeightE against various state-of-the-art baselines.

Cited by 8Open access

Croppable Knowledge Graph Embedding

Yushan Zhu, Wen Zhang, Zhiqiang Liu et al. · arXiv (Cornell University) · 2024

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Generalized Graph Embedding Models

Qiao Liu, Xiaohui Yang, Wan Rui et al. · 2018

Many types of relations in physical, biological, social and information systems can be modeled as homogeneous or heterogeneous concept graphs. Hence, learning from and with graph embeddings has drawn a great deal of research interest recently, but only ad hoc solutions have been obtained this far. In this paper, we conjecture that the one-shot supervised learning mechanism is a bottleneck in improving the performance of the graph embedding learning algorithms, and propose to extend this by introducing a multi-shot unsupervised learning framework. Empirical results on several real-world data set show that the proposed model consistently and significantly outperforms existing state-of-the-art approaches on knowledge base completion and graph based multi-label classification tasks.

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Adversarial Directed Graph Embedding

Shijie Zhu, Jianxin Li, Hao Peng et al. · arXiv (Cornell University) · 2020

Node representation learning for directed graphs is critically important to facilitate many graph mining tasks. To capture the directed edges between nodes, existing methods mostly learn two embedding vectors for each node, source vector and target vector. However, these methods learn the source and target vectors separately. For the node with very low indegree or outdegree, the corresponding target vector or source vector cannot be effectively learned. In this paper, we propose a novel Directed Graph embedding framework based on Generative Adversarial Network, called DGGAN. The main idea is to use adversarial mechanisms to deploy a discriminator and two generators that jointly learn each node's source and target vectors. For a given node, the two generators are trained to generate its fake target and source neighbor nodes from the same underlying distribution, and the discriminator aims to distinguish whether a neighbor node is real or fake. The two generators are formulated into a unified framework and could mutually reinforce each other to learn more robust source and target vectors. Extensive experiments show that DGGAN consistently and significantly outperforms existing state-of-the-art methods across multiple graph mining tasks on directed graphs.

Cited by 3Open access

Process of graph embedding.

Soohwan Jeong (18388644), Jeongseon Kim (189626), Byung Suk Lee (18388647) et al. · Figshare · 2024

We proceeded with graph embedding in two stages. In step 1, the embedding of the node is obtained using the weighted node2vec method. In step 2, final graph embedding is conducted by using the node embedding obtained in step 1 as an feature of each node and feeding it into the GAE embedding model.

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Graph-based Categorical Embedding

Weiwei Wang, Stefano Bromuri, Michel Dumontier · 2023

Categorical features are a challenge for most machine learning algorithms that only accept numerical vectors in input.However, the emergence of graph neural networks is revolutionizing the application of machine learning models to traditional data sets.This is thanks to the possibility of introducing graph relationships amongst features and samples.In this contribution, we describe an algorithm leveraging the assignment matrix of a DiffPool graph neural network to calculate embeddings for categorical features, using as an adjacency matrix the co-occurrence matrix between the categorical values and as nodes feature the one hot encoded categorical values.We show that the algorithm proposed is scalable and presents a competitive performance in three publicly available data sets presenting both numerical and categorical values.

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Graph Embedding Using Dissimilarities

Series in machine perception and artificial intelligence · 2010

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Object graph and embedding.

Benjamin C. Hitz (3921746), Laurence D. Rowe (3921773), Nikhil R. Podduturi (3921761) et al. · Figshare · 2017

The normalized object graph (linked set of documents) stored in PostgreSQL is framed as an expanded JSON-LD document (embedded set of documents) before indexing into Elasticsearch and rendering in JavaScript.

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Motif-Aware Graph Embedding

Nguyen Hoang Thai, Hoang Nguyen, 村田剛志 et al. · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2017

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