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The Distance Function on a Computable Graph [article]

Wesley Calvert, Russell Miller, Jennifer Chubb Reimann
2011 arXiv   pre-print
We apply the techniques of computable model theory to the distance function of a graph.  ...  functions which have nonincreasing computable approximations.  ...  The distance function on a computable graph G is intrinsically n-approximable from above if, for every computable graph H isomorphic to G, the distance function on H is n-approximable from above.  ... 
arXiv:1111.2480v1 fatcat:xydxjnck5jhbvks4k66fiodcki

3D mesh Reeb graph computation using commute-time and diffusion distances

Rachid EL Khoury, Jean-Philippe Vandeborre, Mohamed Daoudi, Atilla M. Baskurt, Robert Sitnik
2012 Three-Dimensional Image Processing (3DIP) and Applications II  
Our mapping function computes a real value for each vertex which provides interesting insights to describe topology structure of the 3D-model.  ...  In this paper, we present an approach for Reeb graph extraction using a novel mapping function.  ...  If we apply a function based on the geodesic distance like the one defined by Tierny et al , 24 the Reeb graph will globally be changed.  ... 
doi:10.1117/12.906724 dblp:conf/3dica/KhouryVD12 fatcat:ang44irxazfl7hsmaazt66m4li

Exact Median Graph Computation Via Graph Embedding [chapter]

Miquel Ferrer, Ernest Valveny, Francesc Serratosa, Horst Bunke
2008 Lecture Notes in Computer Science  
Given a set of graphs, the median graph is defined as the graph which has the smallest sum of distances (SOD) to all the graphs in the set.  ...  In this paper we propose a new approach for the exact computation of the median graph based on graph embedding in vector spaces.  ...  In all these steps we use the graph edit distance under the assumption it is computed using a particular cost function.  ... 
doi:10.1007/978-3-540-89689-0_6 fatcat:vcq2z3l7vbazhfetnuipkedpaa

Additive Angular Margin Loss in Deep Graph Neural Network Classifier For Learning Graph Edit Distance

Nadeem Iqbal Kajla, Malik Muhammad Saad Missen, Muhammad Muzzamil Luqman., Mickael Coustaty, Arif Mehmood, Gyu Sang Choi.
2020 IEEE Access  
CONFLICT OF INTEREST The authors declare that they have no conflict of interest. .  ...  In this work, we propose a method to learn a graph distance between graphs based on Graph Neural Network and local descriptions of a graph.  ...  From the results of FIGURE 6 . 6 Graph Distance computation HD, Soft and HEOMD for Letters MED Dataset using different loss Functions FIGURE 7 . 7 Graph Distance computation HD, Soft and HEOMD for  ... 
doi:10.1109/access.2020.3035886 fatcat:5agu4l3mtzfsxcx5vgvedqloe4

Overlapping community detection in networks based on link partitioning and partitioning around medoids [article]

Alexander Ponomarenko, Leonidas Pitsoulis, Marat Shamshetdinov
2021 arXiv   pre-print
the use of a distance function defined on the set of nodes.  ...  We consider both the commute distance and amplified commute distance as distance functions.  ...  Acknowledgments Authors thank Anna Yaushkina and Nikita Putikhin for the help with implementation of amplified commute distance function and for adding heuristic version of LPAM method.  ... 
arXiv:1907.08731v2 fatcat:kajk2jf55jczfp53udduzsppym

Learning Cost Function for Graph Classification with Open-Set Methods

Rafael de Oliveira Werneck, Romain Raveaux, Salvatore Tabbone, Ricardo da Silva Torres
2019 Pattern Recognition Letters  
These cost functions are embedded into a graph matching-based classifier. The learning algorithm is based on an open-set recognition approach.  ...  In several pattern recognition problems, e↵ective graph matching is of paramount importance. In this paper, we introduce a novel framework to learn discriminative cost functions.  ...  Graph Distance Learning Framework We propose a new framework to learn a discriminative cost function for computing the bipartite graph edit distance between two graphs.  ... 
doi:10.1016/j.patrec.2019.08.010 fatcat:sgjiowpdffhutjvhaj7pih3g2y

Estimating pairwise distances in large graphs

Maria Christoforaki, Torsten Suel
2014 2014 IEEE International Conference on Big Data (Big Data)  
In order to compute a distance bound between two vertices, the proposed methods apply triangle inequalities on top of the precomputed distances between each of these vertices and the landmarks, and then  ...  As features, we use structural attributes of the vertices involved as well as the bounds described above, and we learn a function that predicts the distance between a source and a destination vertex.  ...  Query Processing Time Computing the distance estimate for a pair of vertices (u, v) under this approach is very efficient and depends on the number of features that the distance estimation function uses  ... 
doi:10.1109/bigdata.2014.7004250 dblp:conf/bigdataconf/ChristoforakiS14 fatcat:hh5d5k6mifaobiojhip4iqsnxm

Graph Characteristics from the Ihara Zeta Function [chapter]

Peng Ren, Richard C. Wilson, Edwin R. Hancock
2008 Lecture Notes in Computer Science  
In a previous paper, we have shown that the Ihara zeta function leads to a polynomial characterization of graph structure, and we have shown empirically that the coefficients of the polynomial can be used  ...  This paper shows how to extract permutation invariant graph characteristics from the Ihara zeta function.  ...  Introduction One of the bottlenecks in comparing graphs using graph edit distance [13] is that its computation requires correspondence matches.  ... 
doi:10.1007/978-3-540-89689-0_30 fatcat:ko7oifc4dffslnsvp437fzcu7m

Computing the Barycenter Graph by Means of the Graph Edit Distance

Itziar Bardaji, Miquel Ferrer, Alberto Sanfeliu
2010 2010 20th International Conference on Pattern Recognition  
Our main contribution is that we can apply the method to attributed graphs with any kind of labels in both the nodes and the edges, equipped with a distance function less constrained than in previous approaches  ...  In this paper we propose an extension of the original algorithm which makes use of the graph edit distance in conjunction with the weighted mean of a pair of graphs.  ...  Acknowledgments This work has been supported by the Spanish research programmes Consolider Ingenio 2010 CSD2007-00018.  ... 
doi:10.1109/icpr.2010.241 dblp:conf/icpr/BardajiFS10 fatcat:dcexzsolsfex5ljlyjhmyyjv4y

Adaptation of Eikonal Equation over Weighted Graph [chapter]

Vinh-Thong Ta, Abderrahim Elmoataz, Olivier Lézoray
2009 Lecture Notes in Computer Science  
In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure.  ...  Our formulation of the eikonal equation on weighted graphs generalizes local and nonlocal configurations in the context of image processing and extends this equation for the processing of any unorganized  ...  Then, the distance computation between data is performed by comparing their features that generally depend on a given initial function f 0 ∈H(V ).  ... 
doi:10.1007/978-3-642-02256-2_16 fatcat:ekk3bzrsb5evbcrtjwbml2h2xq

ON THE GRAPH EDIT DISTANCE COST: PROPERTIES AND APPLICATIONS

ALBERT SOLÉ-RIBALTA, FRANCESC SERRATOSA, ALBERTO SANFELIU
2012 International journal of pattern recognition and artificial intelligence  
The use of the Graph Edit Distance tailored to a particular problem requires some application-dependent functions to be defined.  ...  The application of graph edit distance is extensive [24] and therefore numerous algorithms to compute the Graph Edit Distance can be found in the literature, such as [25-29].  ...  (3) Using this definition, Graph Edit Distance depends essentially on and functions. Several definitions of these functions exist. We focus first on the definition of the functions and .  ... 
doi:10.1142/s021800141260004x fatcat:2bplaauyijgp5puvgv3dd3ab6u

A Hausdorff Heuristic for Efficient Computation of Graph Edit Distance [chapter]

Andreas Fischer, Réjean Plamondon, Yvon Savaria, Kaspar Riesen, Horst Bunke
2014 Lecture Notes in Computer Science  
In this paper, we propose a Hausdorff heuristic that employs the approximation algorithm itself as a heuristic function for efficient A* computation of the graph edit distance.  ...  We have recently proposed a quadratic-time approximation of graph edit distance based on Hausdorff matching, which underestimates the true distance.  ...  This work has been supported by the SNSF grant P300P2-151279 to A. Fischer, the NSERC grant RGPIN-915 to R. Plamondon, a Canada Research Chair grant to Y.  ... 
doi:10.1007/978-3-662-44415-3_9 fatcat:rqfjly6nwfhchmtdzd6bzesra4

Non-local Discrete $$\infty $$ ∞ -Poisson and Hamilton Jacobi Equations

Matthieu Toutain, Abderrahim Elmoataz, François Lozes, Alamin Mansouri
2015 Journal of Mathematical Imaging and Vision  
Our motivation is to use this extension to compute distances on any discrete data that can be represented as a weighted graph.  ...  In this paper we propose an adaptation of the ∞-Poisson equation on weighted graphs, and propose a finer expression of the ∞-Laplace operator with gradient terms on weighted graphs, by making the link  ...  Acknowledgements This work was supported under a doctoral grant of the Conseil Régional de Basse Normandie and of the Coeur et Cancer association in collaboration with the Department of Anatomical and  ... 
doi:10.1007/s10851-015-0592-x fatcat:zqeskjh2wvc3jdxwlm4g25zmhm

Edit distance-based kernel functions for structural pattern classification

Michel Neuhaus, Horst Bunke
2006 Pattern Recognition  
A common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance-based nearest-neighbor classifier.  ...  In this paper, we introduce an alternative method for classification using kernel functions based on edit distance.  ...  The authors would also like to thank Barbara Spillmann for preparing the string datasets, and Dr. Jens Gregor for making the Chromosome dataset available.  ... 
doi:10.1016/j.patcog.2006.04.012 fatcat:r6kxeeq4t5exlk3otepkudeznm

Large-scale malware indexing using function-call graphs

Xin Hu, Tzi-cker Chiueh, Kang G. Shin
2009 Proceedings of the 16th ACM conference on Computer and communications security - CCS '09  
To speed up this search, we have developed an efficient method to compute graph similarity that exploits structural and instruction-level information in the underlying malware programs, and a multi-resolution  ...  in a graph database.  ...  Because accessing each index entry involves one graph-distance computation, PIE is a proper metric that captures OVPT's computation cost.  ... 
doi:10.1145/1653662.1653736 dblp:conf/ccs/HuCS09 fatcat:pktjwr2uq5d5lk4pjnfyyttcry
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