Tree Covering within a Graph Kernel Framework for Shape Classification

Shape classification using graphs and skeletons usually involves edition processes in order to reduce the influence of structural noise. On the other hand, graph kernels provide a rich framework in which many classification algorithm may be applied on graphs. However, edit distances cannot be readily used within the kernel machine framework as they generally lead to indefinite kernels. In this paper, we propose a graph kernel based on bags of paths and edit operations which remains positive definite according to the bags. The robustness of this kernel is based on a selection of the paths according to their relevance in the graph. Several experiments prove the efficiency of this approach compared to alternative kernel.

[1]  Pieter Abbeel,et al.  Max-margin Classification of Data with Absent Features , 2008, J. Mach. Learn. Res..

[2]  R. Kass,et al.  Bayesian curve-fitting with free-knot splines , 2001 .

[3]  Fernand Meyer,et al.  Topographic distance and watershed lines , 1994, Signal Process..

[4]  Horst Bunke,et al.  Edit distance-based kernel functions for structural pattern classification , 2006, Pattern Recognit..

[5]  Kaleem Siddiqi,et al.  Hamilton-Jacobi Skeletons , 2002, International Journal of Computer Vision.

[6]  Heiko Hoffmann,et al.  Kernel PCA for novelty detection , 2007, Pattern Recognit..

[7]  Luc Brun,et al.  Hierarchical Bag of Paths for Kernel Based Shape Classification , 2008, SSPR/SPR.

[8]  Alain Rakotomamonjy,et al.  Mining Shock Graphs with Kernels , 2006 .

[9]  Luc Brun,et al.  Edition within a Graph Kernel Framework for Shape Recognition , 2009, GbRPR.

[10]  Kaleem Siddiqi,et al.  Matching Hierarchical Structures Using Association Graphs , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  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.

[12]  Wooi-Boon Goh,et al.  Strategies for shape matching using skeletons , 2008, Comput. Vis. Image Underst..

[13]  Edwin R. Hancock,et al.  A skeletal measure of 2D shape similarity , 2001, Comput. Vis. Image Underst..

[14]  Arthur R. Pope.  Model-Based Object Recognition - A Survey of Recent Research , 1994 .

[15]  David Haussler,et al.  Convolution kernels on discrete structures , 1999 .

[16]  Rolf Niedermeier,et al.  Two fixed-parameter algorithms for Vertex Covering by Paths on Trees , 2008, Inf. Process. Lett..

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

[18]  Ali Shokoufandeh,et al.  Shock Graphs and Shape Matching , 1998, International Journal of Computer Vision.

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

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

[21]  Alain Rakotomamonjy,et al.  Kernel on Bag of Paths For Measuring Similarity of Shapes , 2007, ESANN.