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On the Correlation of Graph Edit Distance and L 1 Distance in the Attribute Statistics Embedding Space [chapter]

Jaume Gibert, Ernest Valveny, Horst Bunke, Alicia Fornés
2012 Lecture Notes in Computer Science  
In this work, we analyse relations between the edit distance in the graph domain and the L1 distance of the attribute statistics based embedding, for which good classification performance has been reported  ...  Graph embeddings in vector spaces aim at assigning a pattern vector to every graph so that the problems of graph classification and clustering can be solved by using data processing algorithms originally  ...  Conclusions In this work we have established a relation between graph edit distance and the L 1 vectorial distance in the attribute statistics embedding space.  ... 
doi:10.1007/978-3-642-34166-3_15 fatcat:cwinatggwzdldoex5c3m5ttike

Graph Self-supervised Learning with Accurate Discrepancy Learning [article]

Dongki Kim, Jinheon Baek, Sung Ju Hwang
2022 arXiv   pre-print
Moreover, we further aim to accurately capture the amount of discrepancy for each perturbed graph using the graph edit distance.  ...  Specifically, we create multiple perturbations of the given graph with varying degrees of similarity and train the model to predict whether each graph is the original graph or a perturbed one.  ...  After that, we learn GNNs to distinguish perturbed graphs from original ones, but also accurately discriminate the original, perturbed, and other graphs in the embedding space with their distances. into  ... 
arXiv:2202.02989v2 fatcat:7x2xshtofvbjlobnqzngkxkosm

A Comparison of Explicit and Implicit Graph Embedding Methods for Pattern Recognition [chapter]

Donatello Conte, Jean-Yves Ramel, Nicolas Sidère, Muhammad Muzzamil Luqman, Benoît Gaüzère, Jaume Gibert, Luc Brun, Mario Vento
2013 Lecture Notes in Computer Science  
In this paper we present a comparison of two implicit and three explicit state of the art graph embedding methodologies.  ...  expensive and efficient state of the art machine learning models of statistical pattern recognition.  ...  Method 3: Attribute Statistics based Embedding The attribute statistics based embedding of graphs is a simple and efficient way of expressing the labelling information stored in nodes and edges of graphs  ... 
doi:10.1007/978-3-642-38221-5_9 fatcat:pzp6r7hjgjbwrmbykpjapbz6t4

On the Use of the Chi-Squared Distance for the Structured Learning of Graph Embeddings

Haifeng Zhao, Antonio Robles-Kelly, Jun Zhou
2011 2011 International Conference on Digital Image Computing: Techniques and Applications  
In this paper, we describe the use of concepts from the areas of structural and statistical pattern recognition for the purposes of recovering a mapping which can be viewed as an operator on the graph  ...  This treatment leads to the recovery of a mapping based upon the graph attributes which is related to the edge-space of the graphs under study.  ...  We recover this embedding making use of the Chi-squared distance and statistical learning techniques.  ... 
doi:10.1109/dicta.2011.78 dblp:conf/dicta/ZhaoRZ11 fatcat:2ll5dyou4zcc5iwn3ut2jqxr7e

A Structured Learning Approach to Attributed Graph Embedding [chapter]

Haifeng Zhao, Jun Zhou, Antonio Robles-Kelly
2010 Lecture Notes in Computer Science  
In this paper, we describe the use of concepts from structural and statistical pattern recognition for recovering a mapping which can be viewed as an operator on the graph attribute-set.  ...  We illustrate the utility of the recovered embedding for shape matching and categorisation on MPEG7 CE-Shape-1 dataset. We also compare our results to those yielded by alternatives.  ...  He is supported by the National Natural Science Foundation of China (NSFC) under No.60775015.  ... 
doi:10.1007/978-3-642-14980-1_6 fatcat:7bzr26l2xfgmbogko6im77cy4a

Spectral embedding of graphs

Bin Luo, Richard C. Wilson, Edwin R. Hancock
2003 Pattern Recognition  
We illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects. Two problems are investigated.  ...  These two studies reveal that both embedding methods result in well-structured view spaces for graph-data extracted from 2D views of 3D objects.  ...  Unfortunately, and for the reasons noted above, the process of embedding graphs in a vector-space is not a straightforward one.  ... 
doi:10.1016/s0031-3203(03)00084-0 fatcat:35bjtqgclbag3kmyo5hhoyexi4

On Palimpsests in Neural Memory: An Information Theory Viewpoint

Lav R. Varshney, Julius Kusuma, Vivek K Goyal
2016 IEEE Transactions on Molecular, Biological and Multi-Scale Communications  
We examine the tradeoff between compression efficiency and malleability cost, under a malleability metric defined with respect to a string edit distance.  ...  a new one.  ...  Now we are concerned with the error-tolerant embedding of an attributed, weighted source adjacency graph into the graph induced by a V * -space edit distance.  ... 
doi:10.1109/tmbmc.2016.2640320 dblp:journals/tmbmc/VarshneyKG16 fatcat:5zutgffzazbpbaxcqkeutlha7u

Concept Drift and Anomaly Detection in Graph Streams

Daniele Zambon, Cesare Alippi, Lorenzo Livi
2018 IEEE Transactions on Neural Networks and Learning Systems  
In addition, we provide a specific implementation of the methodology and evaluate its effectiveness on several detection problems involving attributed graphs representing biological molecules and drawings  ...  The methodology is general and considers a process generating attributed graphs with a variable number of vertices/edges, without the need to assume one-to-one correspondence between vertices at different  ...  A well-known family of algorithms used to assess dissimilarity between graphs relies on the Graph Edit Distance (GED) approach [27] .  ... 
doi:10.1109/tnnls.2018.2804443 pmid:29994077 fatcat:hbulbnosajgptfemcegtenwomi

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

M. Ferrer, E. Valveny, F. Serratosa, K. Riesen, H. Bunke
2010 Pattern Recognition  
In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain.  ...  We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph.  ...  Kaspar Riesen and Horst Bunke like to acknowledge support from the Swiss National Science Foundation (Project 200021-113198/1).  ... 
doi:10.1016/j.patcog.2009.10.013 fatcat:eiia7anyzvd2vd6kbeo2ailydi

Comparing the Preservation of Network Properties by Graph Embeddings [chapter]

Rémi Vaudaine, Rémy Cazabet, Christine Largeron
2020 Lecture Notes in Computer Science  
We show that most of the algorithms are able to recover at most one of the properties and that some algorithms are more sensitive to the embedding space dimension than some others.  ...  Graph embedding is a technique which consists in finding a new representation for a graph usually by representing the nodes as vectors in a low-dimensional real space.  ...  This work has been supported by BITUNAM Project ANR-18-CE23-0004 and IDEXLYON ACADEMICS Project ANR-16-IDEX-0005 of the French National Research Agency.  ... 
doi:10.1007/978-3-030-44584-3_41 fatcat:yhhmurryoff5xde5oldoxzgqha

Approximate graph edit distance computation by means of bipartite graph matching

Kaspar Riesen, Horst Bunke
2009 Image and Vision Computing  
The key advantages of graph edit distance are its high degree of flexibility, which makes it applicable to any type of graph, and the fact that one can integrate domain specific knowledge about object  ...  Its computational complexity, however, is exponential in the number of nodes of the involved graphs. Consequently, exact graph edit distance is feasible for graphs of rather small size only.  ...  (Graph Edit Distance) Let g 1 ¼ ðV 1 ; E 1 ; l 1 ; m 1 Þ be the source and g 2 ¼ ðV 2 ; E 2 ; l 2 ; m 2 Þ the target graph.  ... 
doi:10.1016/j.imavis.2008.04.004 fatcat:3nqeo7teczgjvjao4ogykkedrm

A generic framework for median graph computation based on a recursive embedding approach

M. Ferrer, D. Karatzas, E. Valveny, I. Bardaji, H. Bunke
2011 Computer Vision and Image Understanding  
In order to evaluate the proposed method, we compare it with the set median and with the other state-of-the-art embedding-based methods for the median graph computation.  ...  Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph.  ...  Acknowledgments This work has been supported by the Spanish research programmes Consolider Ingenio 2010 CSD2007-00018, TIN2006-15694-C02-02 and TIN2008-04998 and the fellowship RYC-2009-05031.  ... 
doi:10.1016/j.cviu.2010.12.010 fatcat:m4r23tbp2zep3aij7qv4qzytju

Graph edit distance: Accuracy of local branching from an application point of view

Mostafa Darwiche, Donatello Conte, Romain Raveaux, Vincent T'Kindt
2018 Pattern Recognition Letters  
In the context of graph-based representations, comparing and measuring the dissimilarities between graphs can be done by solving the Graph Edit Distance (GED) problem.  ...  In this work, the focus is on evaluating LocBra with other competitive heuristics available in the literature from an application point of view.  ...  One of the most important problems that belongs to ETGM class is the Graph Edit Distance (GED).  ... 
doi:10.1016/j.patrec.2018.03.033 fatcat:vkqnnyvp7vhxnhbctaa4bfzie4

node2bits: Compact Time- and Attribute-aware Node Representations for User Stitching [article]

Di Jin, Mark Heimann, Ryan Rossi, Danai Koutra
2019 arXiv   pre-print
Extensive experiments on large-scale real networks show that node2bits outperforms traditional techniques and existing works that generate real-valued embeddings by up to 5.16% in F1 score on user stitching  ...  To solve the problem in an application-independent way, we take a heterogeneous network-based approach in which users (nodes) interact with content (e.g., sessions, websites), and may have attributes (  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or other funding parties.  ... 
arXiv:1904.08572v2 fatcat:ialligoyrzfqbhehghnn6vhm2e

Unsupervised Inductive Graph-Level Representation Learning via Graph-Graph Proximity [article]

Yunsheng Bai, Hao Ding, Yang Qiao, Agustin Marinovic, Ken Gu, Ting Chen, Yizhou Sun, Wei Wang
2019 arXiv   pre-print
Experiments on five real graph datasets show that UGRAPHEMB achieves competitive accuracy in the tasks of graph classification, similarity ranking, and graph visualization.  ...  We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity.  ...  C.2 GRAPH EDIT DISTANCE (GED) The edit distance between two graphs (Bunke, 1983 ) G 1 and G 2 is the number of edit operations in the optimal alignments that transform G 1 into G 2 , where an edit operation  ... 
arXiv:1904.01098v2 fatcat:atdqtznunbbo3p6xvywnucsun4
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