Bridging Structure and Feature Representations in Graph Matching

Structures and features are opposite approaches in building representations for object recognition. Bridging the two is an essential problem in pattern recognition as the two opposite types of information are fundamentally different. As dissimilarities can be computed for both the dissimilarity representation can be used to combine the two. Attributed graphs contain structural as well as feature-based information. Neglecting the attributes yields a pure structural description. Isolating the features and neglecting the structure represents objects by a bag of features. In this paper we will show that weighted combinations of dissimilarities may perform better than these two extremes, indicating that these two types of information are essentially different and strengthen each other. In addition we present two more advanced integrations than weighted combining and show that these may improve the classification performances even further.

[1]  Robert P.W. Duin,et al.  PRTools3: A Matlab Toolbox for Pattern Recognition , 2000 .

[2]  Kaspar Riesen,et al.  Feature Ranking Algorithms for Improving Classification of Vector Space Embedded Graphs , 2009, CAIP.

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

[4]  Thomas G. Dietterich,et al.  Solving the Multiple Instance Problem with Axis-Parallel Rectangles , 1997, Artif. Intell..

[5]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

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

[7]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[8]  Anil K. Jain,et al.  Statistical Pattern Recognition: A Review , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

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

[10]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[11]  Thomas Gärtner,et al.  On Graph Kernels: Hardness Results and Efficient Alternatives , 2003, COLT.

[12]  Robert P. W. Duin,et al.  A Matlab Toolbox for Pattern Recognition , 2004 .

[13]  Terry Caelli,et al.  An eigenspace projection clustering method for inexact graph matching , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[15]  Thomas Gärtner,et al.  Multi-Instance Kernels , 2002, ICML.

[16]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[17]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[18]  Horst Bunke,et al.  Syntactic and Structural Pattern Recognition , 1988, NATO ASI Series.

[19]  Robert P. W. Duin,et al.  Dissimilarity representations allow for building good classifiers , 2002, Pattern Recognit. Lett..

[20]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[21]  Thomas Gärtner,et al.  Cyclic pattern kernels for predictive graph mining , 2004, KDD.

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

[23]  Kaspar Riesen,et al.  Bipartite Graph Matching for Computing the Edit Distance of Graphs , 2007, GbRPR.

[24]  Kaspar Riesen,et al.  Efficient Suboptimal Graph Isomorphism , 2009, GbRPR.

[25]  Wan-Jui Lee,et al.  An Inexact Graph Comparison Approach in Joint Eigenspace , 2008, SSPR/SPR.

[26]  Thomas Hofmann,et al.  Multiple instance learning with generalized support vector machines , 2002, AAAI/IAAI.

[27]  T. B. Boffey,et al.  Applied Graph Theory , 1973 .

[28]  R. Duin,et al.  The dissimilarity representation for pattern recognition , a tutorial , 2009 .

[29]  Kaspar Riesen,et al.  Recent advances in graph-based pattern recognition with applications in document analysis , 2011, Pattern Recognit..

[30]  Tomás Lozano-Pérez,et al.  A Framework for Multiple-Instance Learning , 1997, NIPS.

[31]  James R. Foulds,et al.  Revisiting Multiple-Instance Learning Via Embedded Instance Selection , 2008, Australasian Conference on Artificial Intelligence.

[32]  Robert Hecht Nielsen,et al.  Applied Graph Theory in Computer Vision and Pattern Recognition , 2007, Studies in Computational Intelligence.

[33]  Horst Bunke,et al.  Syntactic and structural pattern recognition : theory and applications , 1990 .

[34]  Hisashi Kashima,et al.  Marginalized Kernels Between Labeled Graphs , 2003, ICML.

[35]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[36]  Robert P. W. Duin,et al.  A Generalized Kernel Approach to Dissimilarity-based Classification , 2002, J. Mach. Learn. Res..

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

[38]  Kaspar Riesen,et al.  Graph Classification Based on Dissimilarity Space Embedding , 2008, SSPR/SPR.

[39]  Kaspar Riesen,et al.  Cluster Ensembles Based on Vector Space Embeddings of Graphs , 2009, MCS.

[40]  Hans-Peter Kriegel,et al.  Protein function prediction via graph kernels , 2005, ISMB.

[41]  N. V. Vinodchandran,et al.  Kernels for Generalized Multiple-Instance Learning , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Yixin Chen,et al.  MILES: Multiple-Instance Learning via Embedded Instance Selection , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[43]  Edwin R. Hancock,et al.  Pattern Vectors from Algebraic Graph Theory , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  Paul A. Viola,et al.  Multiple Instance Boosting for Object Detection , 2005, NIPS.

[45]  Edwin R. Hancock,et al.  Clustering and Embedding Using Commute Times , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Jun Wang,et al.  Solving the Multiple-Instance Problem: A Lazy Learning Approach , 2000, ICML.

[47]  Josef Kittler,et al.  Pattern recognition : a statistical approach , 1982 .

[48]  Robert P. W. Duin,et al.  The Dissimilarity Representation for Pattern Recognition - Foundations and Applications , 2005, Series in Machine Perception and Artificial Intelligence.

[49]  Thomas Gärtner Predictive Graph Mining with Kernel Methods , 2005 .

[50]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[51]  Hans-Peter Kriegel,et al.  Shortest-path kernels on graphs , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[52]  Ujjwal Maulik,et al.  Advanced Methods for Knowledge Discovery from Complex Data , 2005 .