A Short Survey of Recent Advances in Graph Matching

Yan, Junchi; Yin, Xu-Cheng; Lin, Weiyao; Deng, Cheng; Zha, Hongyuan; Yang, Xiaokang

doi:10.1145/2911996.2912035

Cited by 146 publications

(100 citation statements)

References 133 publications

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“…Particular aspects of graph querying have also been surveyed; for example, works by Bunke [2000], Gallagher [2006], Riesen et al [2010], Livi and Rizzi [2013], and Yan et al [2016] deal with particular aspects of graph pattern matching, while Yu and Cheng [2010] concentrate on graph reachability queries. Again, however, all such works have a narrower focus than our survey.…”

Section: Introductionmentioning

confidence: 99%

Foundations of Modern Query Languages for Graph Databases

et al. 2017

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We survey foundational features underlying modern graph query languages. We first discuss two popular graph data models: edge-labelled graphs, where nodes are connected by directed, labelled edges; and property graphs, where nodes and edges can further have attributes. Next we discuss the two most fundamental graph querying functionalities: graph patterns and navigational expressions. We start with graph patterns, in which a graph-structured query is matched against the data. Thereafter we discuss navigational expressions, in which patterns can be matched recursively against the graph to navigate paths of arbitrary length; we give an overview of what kinds of expressions have been proposed, and how they can be combined with graph patterns. We also discuss several semantics under which queries using the previous features can be evaluated, what effects the selection of features and semantics has on complexity, and offer examples of such features in three modern languages that are used to query graphs: SPARQL, Cypher and Gremlin. We conclude by discussing the importance of formalisation for graph query languages; a summary of what is known about SPARQL, Cypher and Gremlin in terms of expressivity and complexity; and an outline of possible future directions for the area.

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Section: Introductionmentioning

confidence: 99%

Foundations of Modern Query Languages for Graph Databases

et al. 2017

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“…j ), and K i1j1;i2j2 measures the edge affinity calculated with edge attributes as Φ e (e (1) i1i2 , e (2) j1,j2 ). K ∈ R mn×mn is called the affinity matrix of G 1 and G 2 .…”

Section: Definition Of Gm Problemmentioning

confidence: 99%

“…Graph matching (GM) is widely used to find node-to-node correspondence [1,2] between graph-structured data in many computer vision and pattern recognition tasks, such as shape matching and retrieval [3,4], object categorization [5], action recognition [6], and structure from motion [7], to name a few. In these applications, real-world data are generally represented as abstract graphs equipped with node attributes (e.g., SIFT descriptor, shape context) and edge attributes (e.g., relationships between nodes).…”

Section: Introductionmentioning

confidence: 99%

“…Although the past decades have witnessed remarkable progresses in GM [1], there are still many challenges with respect to both computational difficulty and formulation expression. Specifically, as widely used, GM that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP) [12], among which Lawler's QAP [13] and Koopmans-Beckmann's QAP [14] are two common formulations.…”

Section: Introductionmentioning

confidence: 99%

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A Functional Representation for Graph Matching

Wang

Xue

Zhang

et al. 2019

IEEE Trans. Pattern Anal. Mach. Intell.

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Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. In this paper, we present a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities of corresponding algorithms. To achieve these goals, we represent a graph endowed with edge attributes by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence between graphs can be represented as a linear representation map of that functional. Specifically, we reformulate the linear functional representation map as a new parameterization for Euclidean graph matching, which is associative with geometric parameters for graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence and geometric deformations simultaneously. The use of the representation of edge attributes rather than the affinity matrix enables us to reduce the space complexity by two orders of magnitudes. Furthermore, we propose an efficient optimization strategy with low time complexity to optimize the objective function. The experimental results on both synthetic and real-world datasets demonstrate that the proposed FRGM can achieve state-of-the-art performance.

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“…The above noisy induced subgraph detection problem depends greatly on the definition of "best fitting" employed. Our approach, generalizing [36] to the multiplex setting, will employ the multiplex template H to search the multiplex background graph G for possible matches, with goodness of fit measured via a multiplex formulation of the classical graph matching problem (see [9,17,15,40] for excellent reviews of the voluminous graph matching literature).…”

Section: Introductionmentioning

confidence: 99%

Multiplex graph matching matched filters

Pantazis

Sussman

Park

et al. 2019

2019 IEEE International Conference on Big Data (Big Data)

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We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the framework of [36] to the multiplex setting, leverages a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels.for a definition of multiplex isomorphism), accounting for the reality that relatively large, complex subgraph templates may only errorfully occur in the larger background network. These errors may be due to missing edges/vertices in the template or background, and arise in a variety of real data settings [34]. The subgraph isomorphism problem-given a template A, determine if an isomorphic copy of A exists in a larger network B and find the isomorphic copy (or copies) if it exists-has been the subject of voluminous research in the monoplex (i.e., single layer) setting, with approaches based on efficient tree search [38], color coding [3, 2], graph homomorphisms [18], rule-based/filter-based matchings [10,29], among others; for a survey of the literature circa 2012, see [24]. In contrast, the problem of multilayer homomorphic/isomorphic subgraph detection is still in its relative infancy, with comparatively fewer existing methods in the literature; see, for example, [41,37,29]. Notation: The following notation will be used throughout. For an integer n > 0, we will define [n] := {1, 2, . . . , n}, J n to be the n × n hollow matrix with all off-diagonal entries identically set to 1, 0 n to be the n × n matrix with all entries identically set to 0,

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A Short Survey of Recent Advances in Graph Matching

Cited by 146 publications

References 133 publications

Foundations of Modern Query Languages for Graph Databases

Foundations of Modern Query Languages for Graph Databases

A Functional Representation for Graph Matching

Multiplex graph matching matched filters

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