Improving vector space embedding of graphs through feature selection algorithms

Graph based pattern representation offers a versatile alternative to vectorial data structures. Therefore, a growing interest in graphs can be observed in various fields. However, a serious limitation in the use of graphs is the lack of elementary mathematical operations in the graph domain, actually required in many pattern recognition algorithms. In order to overcome this limitation, the present paper proposes an embedding of a given graph population in a vector space R^n. The key idea of this embedding approach is to interpret the distances of a graph g to a number of prototype graphs as numerical features of g. In previous works, the prototypes were selected beforehand with heuristic selection algorithms. In the present paper we take a more fundamental approach and regard the problem of prototype selection as a feature selection or dimensionality reduction problem, for which many methods are available. With several experiments we show the feasibility of graph embedding based on prototypes obtained from such feature selection algorithms and demonstrate their potential to outperform previous approaches.

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

[2]  Jason Weston,et al.  Gene Selection for Cancer Classification using Support Vector Machines , 2002, Machine Learning.

[3]  Uchida Seiichi,et al.  Part-based recognition of handwritten digits -- * , 2010 .

[4]  Horst Bunke,et al.  Graph Edit Distance with Node Splitting and Merging, and Its Application to Diatom Idenfication , 2003, GbRPR.

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

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

[7]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[8]  Horst Bunke,et al.  A Graph-Theoretic Approach to Enterprise Network Dynamics (Progress in Computer Science and Applied Logic (PCS)) , 2006 .

[9]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2004 .

[10]  J. Kazius,et al.  Derivation and validation of toxicophores for mutagenicity prediction. , 2005, Journal of medicinal chemistry.

[11]  Horst Bunke,et al.  Self-organizing maps for learning the edit costs in graph matching , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Horst Bunke,et al.  Matching graphs with unique node labels , 2004, Pattern Analysis and Applications.

[13]  Horst Bunke,et al.  Transforming Strings to Vector Spaces Using Prototype Selection , 2006, SSPR/SPR.

[14]  W. Wallis,et al.  A Graph-Theoretic Approach to Enterprise Network Dynamics , 2006 .

[15]  Tatsuya Akutsu,et al.  Graph Kernels for Molecular Structure-Activity Relationship Analysis with Support Vector Machines , 2005, J. Chem. Inf. Model..

[16]  Kaspar Riesen,et al.  Fast Suboptimal Algorithms for the Computation of Graph Edit Distance , 2006, SSPR/SPR.

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

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

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

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

[21]  Kaspar Riesen,et al.  Graph Classification and Clustering Based on Vector Space Embedding , 2010, Series in Machine Perception and Artificial Intelligence.

[22]  Zaïd Harchaoui,et al.  Image Classification with Segmentation Graph Kernels , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[23]  Igor V. Tetko,et al.  Gene selection from microarray data for cancer classification - a machine learning approach , 2005, Comput. Biol. Chem..

[24]  Horst Bunke,et al.  Automatic learning of cost functions for graph edit distance , 2007, Inf. Sci..

[25]  Kaspar Riesen,et al.  Non-linear Transformations of Vector Space Embedded Graphs , 2008, PRIS.

[26]  Ronald R. Coifman,et al.  Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators , 2005, NIPS.

[27]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[28]  Edwin R. Hancock,et al.  Spectral embedding of graphs , 2003, Pattern Recognit..

[29]  Josep Lladós,et al.  Graph Matching Versus Graph Parsing In Graphics Recognition - A Combined Approach , 2004, Int. J. Pattern Recognit. Artif. Intell..

[30]  Pierre Baldi,et al.  Graph kernels for chemical informatics , 2005, Neural Networks.

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

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

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

[34]  Hong Yan,et al.  Recognition of handprinted Chinese characters by constrained graph matching , 1998, Image Vis. Comput..

[35]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[36]  Horst Bunke,et al.  On Median Graphs: Properties, Algorithms, and Applications , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[38]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

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

[40]  Usama M. Fayyad,et al.  Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning , 1993, IJCAI.

[41]  Antje Chang,et al.  BRENDA , the enzyme database : updates and major new developments , 2003 .

[42]  Kaspar Riesen,et al.  Reducing the Dimensionality of Vector Space Embeddings of Graphs , 2007, MLDM.

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

[44]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

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

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

[47]  Ron Kohavi,et al.  Wrappers for Feature Subset Selection , 1997, Artif. Intell..

[48]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[49]  Josef Kittler,et al.  Floating search methods in feature selection , 1994, Pattern Recognit. Lett..

[50]  Theodosios Pavlidis,et al.  A Shape Analysis Model with Applications to a Character Recognition System , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[51]  Abraham Kandel,et al.  Classification Of Web Documents Using Graph Matching , 2004, Int. J. Pattern Recognit. Artif. Intell..

[52]  Bernard Haasdonk,et al.  Feature space interpretation of SVMs with indefinite kernels , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.