Improved local search for graph edit distance

Boria, Nicolas; Blumenthal, David B.; Bougleux, Sébastien; Brun, Luc

doi:10.1016/j.patrec.2019.10.028

Cited by 17 publications

(7 citation statements)

References 31 publications

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“…While GED is very popular for many graph mining problems, exact GED computation is NP-hard. Therefore, many different heuristic algorithms are proposed to compute approximate solutions [19], [29]- [32]. Among them, local search based algorithms [29], [30] provide the tightest upper bounds for GED.…”

Section: ) Graph Classificationmentioning

confidence: 99%

Graph Classification via Heat Diffusion on Simplicial Complexes

Aktaş

Akbaş

2021

IEEE Access

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In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent vertex-labeled graphs as simplex-weighted super-graphs. We then define the diffusion Fréchet function over their simplices to encode the higher-order network topology and finally reach our goal by combining the function values with machine learning algorithms. Our experiments on real-world bioinformatics networks show that using diffusion Fréchet function on simplices is promising in graph classification and more effective than the baseline methods. To the best of our knowledge, this paper is the first paper in the literature using heat diffusion on higherdimensional simplices in a graph mining problem. We believe that our method can be extended to different graph mining domains, not only the graph classification problem.

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Section: ) Graph Classificationmentioning

confidence: 99%

Graph Classification via Heat Diffusion on Simplicial Complexes

Aktaş

Akbaş

2021

IEEE Access

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“…For the inexact graph matching problem, the most known paradigms are a graph edit distance [12][13][14], b graph kernels and embedding [15][16][17][18], c spectral algorithms [3,4,19,20] and d algorithms based on deep learning [21,22]. The reader can refer to the surveys [23][24][25][26] for more details on graph matching algorithms classification.…”

Section: Related Workmentioning

confidence: 99%

Some Consistency Rules for Graph Matching

Benreguia

Moumen

2021

SN COMPUT. SCI.

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Graph matching is a comparison process of two objects represented as graphs through finding a correspondence between vertices and edges. This process allows defining a similarity degree (or dissimilarity) between the graphs. Generally, graph matching is used for extracting, finding and retrieving any information or sub-information that can be represented by graphs. In this paper, a new consistency rule is proposed to tackle with various problems of graph matching. After, using the proposed rule as a necessary and sufficient condition for the graph isomorphism, we generalize it for subgraph isomorphism, homomorphism and for an example of inexact graph matching. To determine whether there is a matching or not, a backtracking algorithm called CRGI2 is presented who checks the consistency rule by exploring the overall search space. The tree-search is consolidated with a tree pruning technique that eliminates the unfruitful branches as early as possible. Experimental results show that our algorithm is efficient and applicable for a real case application in the information retrieval field. On the efficiency side, due to the ability of the proposed rule to eliminate as early as possible the incorrect solutions, our algorithm outperforms the existing algorithms in the literature. For the application side, the algorithm has been successfully tested for querying a real dataset that contains a large set of e-mail messages.

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“…The algorithm K-REFINE [12] is a straightforward extension of the algorithm REFINE presented in the previous section. Let π ∈ Π (G, H) be an initial node map and K ∈ N ≥2 be a constant.…”

Section: The Algorithm K-refinementioning

confidence: 99%

“…The RANDPOST framework initially proposed in [13] and refined in [12] aims at extending the the MULTI-START framework by running it several times in a row, and using the information contained in the computed local optima computed so far in order to produce better initializations. In addition to the two parameters K and ρ of MULTI-START, RANDPOST requires two parameters: the number of iterations L ∈ N and a penalty parameter η ∈ [0, 1].…”

Section: The Extension Randpostmentioning

confidence: 99%

“…-Meta-parameters for K-REFINE: We ran K-REFINE with swap size K := 3. We hence followed the suggestion in [12], where it is highlighted that K > 3 leads to an enormous blowup of K-REFINE's runtime on larger graphs. -Meta-parameters for BP-BEAM and IBP-BEAM: As suggested in [56] and [27], we set the beam size employed by BP-BEAM and IBP-BEAM to K := 5 and the number of iterations employed by IBP-BEAM to I := 20.…”

Section: Choice Of Options and Parametersmentioning

confidence: 99%

See 1 more Smart Citation

Comparing heuristics for graph edit distance computation

Blumenthal¹,

Boria²,

Gamper³

et al. 2019

The VLDB Journal

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Because of its flexibility, intuitiveness, and expressivity, the graph edit distance (GED) is one of the most widely used distance measures for labeled graphs. Since exactly computing GED is NP-hard, over the past years, various heuristics have been proposed. They use techniques such as transformations to the linear sum assignment problem with error-correction, local search, and linear programming to approximate GED via upper or lower bounds. In this paper, we provide a systematic overview of the most important heuristics. Moreover, we empirically evaluate all compared heuristics within an integrated implementation.

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Improved local search for graph edit distance

Cited by 17 publications

References 31 publications

Graph Classification via Heat Diffusion on Simplicial Complexes

Graph Classification via Heat Diffusion on Simplicial Complexes

Some Consistency Rules for Graph Matching

Comparing heuristics for graph edit distance computation

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