Greedy Graph Edit Distance

In pattern recognition and data mining applications, where the underlying data is characterized by complex structural relationships, graphs are often used as a formalism for object representation. Yet, the high representational power and flexibility of graphs is accompanied by a significant increase of the complexity of many algorithms. For instance, exact computation of pairwise graph dissimilarity, i.e.i?źdistance, can be accomplished in exponential time complexity only. A previously introduced approximation framework reduces the problem of graph comparison to an instance of a linear sum assignment problem which allows graph dissimilarity computation in cubic time. The present paper introduces an extension of this approximation framework that runs in quadratic time. We empirically confirm the scalability of our extension with respect to the run time, and moreover show that the quadratic approximation leads to graph dissimilarities which are sufficiently accurate for graph based pattern classification.

[1]  Kaspar Riesen,et al.  Approximate graph edit distance computation by means of bipartite graph matching , 2009, Image Vis. Comput..

[2]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[3]  Horst Bunke,et al.  Bridging the Gap between Graph Edit Distance and Kernel Machines , 2007, Series in Machine Perception and Artificial Intelligence.

[4]  Mario Vento,et al.  Graph Matching and Learning in Pattern Recognition in the Last 10 Years , 2014, Int. J. Pattern Recognit. Artif. Intell..

[5]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Ming S. Hung,et al.  Technical Note - A Polynomial Simplex Method for the Assignment Problem , 1983, Oper. Res..

[7]  V. Srinivasan,et al.  Cost operator algorithms for the transportation problem , 1977, Math. Program..

[8]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

[9]  D. Bertsekas The auction algorithm: A distributed relaxation method for the assignment problem , 1988 .

[10]  Kaspar Riesen,et al.  Graph Classification Based on Vector Space Embedding , 2009, Int. J. Pattern Recognit. Artif. Intell..

[11]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[12]  David Avis,et al.  A survey of heuristics for the weighted matching problem , 1983, Networks.

[13]  Lawrence B. Holder,et al.  Mining Graph Data , 2006 .

[14]  Ming S. Hung,et al.  Solving the Assignment Problem by Relaxation , 1980, Oper. Res..

[15]  J. Munkres ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[16]  Edwin R. Hancock,et al.  Structural, Syntactic, and Statistical Pattern Recognition, Joint IAPR International Workshop, SSPR&SPR 2010, Cesme, Izmir, Turkey, August 18-20, 2010. Proceedings , 2010, SSPR/SPR.

[17]  Ernest Valveny,et al.  Report on the Second Symbol Recognition Contest , 2005, GREC.

[18]  Celso C. Ribeiro,et al.  A Randomized Heuristic for Scene Recognition by Graph Matching , 2004, WEA.

[19]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[20]  Horst Bunke,et al.  Inexact graph matching for structural pattern recognition , 1983, Pattern Recognit. Lett..

[21]  Christine Solnon,et al.  Reactive Tabu Search for Measuring Graph Similarity , 2005, GbRPR.

[22]  Horst Bunke,et al.  On Graphs with Unique Node Labels , 2003, GbRPR.

[23]  Horst Bunke,et al.  An Error-Tolerant Approximate Matching Algorithm for Attributed Planar Graphs and Its Application to Fingerprint Classification , 2004, SSPR/SPR.

[24]  S. V. N. Vishwanathan,et al.  Graph kernels , 2007 .

[25]  Ravindra K. Ahuja,et al.  The Scaling Network Simplex Algorithm , 1992, Oper. Res..

[26]  A. Volgenant,et al.  A shortest augmenting path algorithm for dense and sparse linear assignment problems , 1987, Computing.

[27]  Alfred O. Hero,et al.  A binary linear programming formulation of the graph edit distance , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Kaspar Riesen,et al.  Computing Upper and Lower Bounds of Graph Edit Distance in Cubic Time , 2014, ANNPR.

[29]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[30]  J. Orlin On the simplex algorithm for networks and generalized networks , 1983 .

[31]  Francesc Serratosa,et al.  Active Graph Matching Based on Pairwise Probabilities between Nodes , 2012, SSPR/SPR.

[32]  R. Luchsinger Der objektive Nachweis des Geruchsvermögens (Olfacto-Pupillarreflex) , 1945 .

[33]  Abraham Kandel,et al.  Graph-Theoretic Techniques for Web Content Mining , 2005, Series in Machine Perception and Artificial Intelligence.

[34]  Konstantinos Paparrizos,et al.  A Dual Forest Algorithm for the Assignment Problem , 1990, Applied Geometry And Discrete Mathematics.

[35]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[36]  Kaspar Riesen,et al.  IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning , 2008, SSPR/SPR.

[37]  Jerome M. Kurtzberg,et al.  On Approximation Methods for the Assignment Problem , 1962, JACM.

[38]  Mauro Dell'Amico,et al.  8. Quadratic Assignment Problems: Algorithms , 2009 .

[39]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[40]  Mustafa Akgül,et al.  A sequential dual simplex algorithm for the linear assignment problem , 1988 .

[41]  Thomas Gärtner,et al.  Kernels for structured data , 2008, Series in Machine Perception and Artificial Intelligence.

[42]  Rainer E. Burkard,et al.  Linear Assignment Problems and Extensions , 1999, Handbook of Combinatorial Optimization.

[43]  R. Jonker,et al.  Improving the Hungarian assignment algorithm , 1986 .