A Novel Software Toolkit for Graph Edit Distance Computation

Riesen, Kaspar; Emmenegger, Sandro; Bunke, Horst

doi:10.1007/978-3-642-38221-5_15

Cited by 66 publications

(33 citation statements)

References 19 publications

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“…We consider also the dissimilarity representation, Dissimilarity Repr., as further element of comparison [6]. Experiments in the graph domain are performed by monitoring statistic d(µ[g 0 ], g t ), where g 0 is a set of training graphs on which we estimated µ[Q] and d(·, ·) is the graph edit distance [8]. The experiments denoted with Spherical Man., Euclidean Man., and Hyperbolic Man.…”

Section: Methodsmentioning

confidence: 99%

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Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings

Zambon

Livi

Alippi

2018

2018 International Joint Conference on Neural Networks (IJCNN)

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Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data representation possibly characterised by convenient geometric properties. Euclidean spaces are by far the most widely used embedding spaces, thanks to their well-understood structure and large availability of consolidated inference methods. However, recent research demonstrated that many types of complex data (e.g., those represented as graphs) are actually better described by non-Euclidean geometries. Here, we investigate how embedding graphs on constant-curvature manifolds (hyper-spherical and hyperbolic manifolds) impacts on the ability to detect changes in sequences of attributed graphs. The proposed methodology consists in embedding graphs into a geometric space and perform change detection there by means of conventional methods for numerical streams. The curvature of the space is a parameter that we learn to reproduce the geometry of the original application-dependent graph space. Preliminary experimental results show the potential capability of representing graphs by means of curved manifold, in particular for change and anomaly detection problems.

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Section: Methodsmentioning

confidence: 99%

“…Embedding distortion of Equation(8) observed for different curvatures κ. The logarithm of the distortion is computed in the first step of the training stage.…”

mentioning

confidence: 99%

Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings

Zambon

Livi

Alippi

2018

2018 International Joint Conference on Neural Networks (IJCNN)

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“…For example, if we want to retrieve ΨD [14] (suppose that the subscript starts from 0 and b = 4) shown in Figure 6 As discussed above, the core operation in a succinct q-gram tree is to calculate ΨX [j] by formula (2), i.e., the decompress operation. In order to accelerate the decompress process, we use the look up table technique proposed in [5] to ensure that the decompress operation takes a constant time.…”

Section: Access To ψXmentioning

confidence: 99%

“…Then we only need to perform the query on the q-gram trees Ti,j built on these subregions Ai,j satisfying Ai,j ⊆ Q h in lines 3-5. For each candidate graph g in Cand , we can use the methods in [10,14,24] to compute the edit distance between g and h to seek for the required graphs.…”

Section: Query Algorithmmentioning

confidence: 99%

MSQ-Index: A Succinct Index for Fast Graph Similarity Search

Chen

Huo

Huan

et al. 2021

IEEE Trans. Knowl. Data Eng.

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Graph similarity search has received considerable attention in many applications, such as bioinformatics, data mining, pattern recognition, and social networks. Existing methods for this problem have limited scalability because of the huge amount of memory they consume when handling very large graph databases with millions or billions of graphs.In this paper, we study the problem of graph similarity search under the graph edit distance constraint. We present a space-efficient index structure based upon the q-gram tree that incorporates succinct data structures and hybrid encoding to achieve improved query time performance with minimal space usage. Specifically, the space usage of our index requires only 5%-15% of the previous state-of-the-art indexing size on the tested data while at the same time achieving 2-3 times acceleration in query time with small data sets. We also boost the query performance by augmenting the global filter with range search, which allows us to perform a query in a reduced region. In addition, we propose two effective filters that combine degree structures and label structures. Extensive experiments demonstrate that our proposed approach is superior in space and competitive in filtering to the state-of-the-art approaches. To the best of our knowledge, our index is the first in-memory index for this problem that successfully scales to cope with the large dataset of 25 million chemical structure graphs from the PubChem dataset.

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“…The edit path γ corresponds to an optimal edit path. GED has been widely used by the structural pattern recognition community [15,4,11,12] despite the fact that such distance comes along with several drawbacks. First of all, computing the GED of two graphs requires to find a path having a minimal cost among all possible paths, which is a NP-complete problem [8].…”

Section: Introductionmentioning

confidence: 99%

Approximating Graph Edit Distance Using GNCCP

Gaüzère

Bougleux

Brun

2016

Lecture Notes in Computer Science

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Abstract. The graph edit distance (GED) is a flexible and widely used dissimilarity measure between graphs. Computing the GED between two graphs can be performed by solving a quadratic assignment problem (QAP). However, the problem is NP complete hence forbidding the computation of the optimal GED on large graphs. To tackle this drawback, recent heuristics are based on a linear approximation of the initial QAP formulation. In this paper, we propose a method providing a better local minimum of the QAP formulation than our previous proposition based on IPFP. We adapt a convex concave regularization scheme initially designed for graph matching which allows to reach better local minimum and avoids the need of an initialization step. Several experiments demonstrate that our method outperforms previous methods in terms of accuracy, with a time still much lower than the computation of a GED.

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A Novel Software Toolkit for Graph Edit Distance Computation

Cited by 66 publications

References 19 publications

Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings

Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings

MSQ-Index: A Succinct Index for Fast Graph Similarity Search

Approximating Graph Edit Distance Using GNCCP

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