Generalized median graph computation by means of graph embedding in vector spaces

Ferrer, Miquel; Valveny, Ernest; Serratosa, Francesc; Riesen, Kaspar; Bunke, Horst

doi:10.1016/j.patcog.2009.10.013

Cited by 84 publications

(79 citation statements)

References 18 publications

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“…We conclude that for the letter datasets, the approximated algorithms used for median and barycenter computation, although they have been experimentally validated [5,6], fail to give satisfactory results. Let us remark that these databases suffer from a high level of distortion, potentiated by the fact that the graphs have few nodes.…”

Section: Distance To Prototypementioning

confidence: 93%

“…In this algorithm from [6], once the median vectorp, is computed, the two closest points, p 1 and p 2 without lost of generality, are used to obtain the approximate median. The approximate generalized Median Graph,g, is then the weighted mean of g 1 and g 2 , with a =…”

Section: Median Graph Via Graph Embeddingmentioning

confidence: 99%

“…This computation consists on generating an intermediate weighted mean using two of the three points followed by a second and definitive weighted mean which makes use of the third point and the previous weighted mean. The procedure, referred to as triangulation embedding (MTE), was proposed and explained in [6].…”

Section: Median Graph Via Graph Embeddingmentioning

confidence: 99%

“…Table 2 shows the number of distances and weighted means that need to be computed for each of the methods, where n is the number of graphs in the given set S. The embedding procedure has been shown to be the only method for the Generalized Median Graph computation potentially applicable to real world problems, due to its lower computational demand [6]. Still, the embedding step (Step I) requires the computation of all the pairwise distances of the graphs in the given set S. That means that the number of distances computed is quadratic on the number n of graphs.…”

Section: Algorithmical Considerationsmentioning

confidence: 99%

See 3 more Smart Citations

A Comparison between Two Representatives of a Set of Graphs: Median vs. Barycenter Graph

Bardají

Ferrer

Sanfeliu

2010

Lecture Notes in Computer Science

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Abstract. In this paper we consider two existing methods to generate a representative of a given set of graphs, that satisfy the following two conditions. On the one hand, that they are applicable to graphs with any kind of labels in nodes and edges and on the other hand, that they can handle relatively large amount of data. Namely, the approximated algorithms to compute the Median Graph via graph embedding and a new method to compute the Barycenter Graph. Our contribution is to give a new algorithm for the barycenter computation and to compare it to the median Graph. To compare these two representatives, we take into account algorithmic considerations and experimental results on the quality of the representative and its robustness, on several datasets.

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Section: Distance To Prototypementioning

confidence: 93%

Section: Median Graph Via Graph Embeddingmentioning

confidence: 99%

Section: Median Graph Via Graph Embeddingmentioning

confidence: 99%

Section: Algorithmical Considerationsmentioning

confidence: 99%

See 2 more Smart Citations

A Comparison between Two Representatives of a Set of Graphs: Median vs. Barycenter Graph

Bardají

Ferrer

Sanfeliu

2010

Lecture Notes in Computer Science

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“…It is easy to understand that these two definitions of representative of a cluster and the sample-to-cluster dissimilarity strictly depend on the domain of the problem. For example, if X=G, where G is a set of graphs, the problem of deriving a representative graph is known as the set median graph computation [1], [5], [6].…”

Section: A Clustering Structured Data By K-meansmentioning

confidence: 99%

On the Problem of Modeling Structured Data with the MinSOD Representative

Vescovo¹,

Livi²,

Massimo³

et al. 2014

IJCTE

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Abstract-The possibility to face pattern recognition problems directly on structured domains (e.g., multimedia data, strings, graphs) is fundamental to the effective solution of many interesting applications. In this paper, we deal with a clustering problem defined in the string domain, focusing on the problem of cluster representation in data domains where only a dissimilarity measure can be fixed. To this aim, we adopt the MinSOD (Minimum Sum of Distances) cluster representation technique, which defines the representative as the element of the cluster minimizing the sum of dissimilarities from all the other elements in the considered set. Since the precise computation of the MinSOD have a high computational cost, we propose a suboptimal procedure consisting in computing the representative of the cluster considering only a reduced pool of samples, instead of the whole set of objects in the cluster. We have carried out some tests in order to ascertain the sensitivity of the clustering procedure with respect to the number of samples in the pool used to compute the MinSOD. Results show a good robustness of the proposed procedure. The implementations are available as part of the SPARE library, which is available as an open source project.

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An Overview of Symbol Recognition

Tabbone

Terrades

2014

Handbook of Document Image Processing and Recognition

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Generalized median graph computation by means of graph embedding in vector spaces

Cited by 84 publications

References 18 publications

A Comparison between Two Representatives of a Set of Graphs: Median vs. Barycenter Graph

A Comparison between Two Representatives of a Set of Graphs: Median vs. Barycenter Graph

On the Problem of Modeling Structured Data with the MinSOD Representative

An Overview of Symbol Recognition

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