Feature selection on node statistics based embedding of graphs

Representing a graph with a feature vector is a common way of making statistical machine learning algorithms applicable to the domain of graphs. Such a transition from graphs to vectors is known as graph embedding. A key issue in graph embedding is to select a proper set of features in order to make the vectorial representation of graphs as strong and discriminative as possible. In this article, we propose features that are constructed out of frequencies of node label representatives. We first build a large set of features and then select the most discriminative ones according to different ranking criteria and feature transformation algorithms. On different classification tasks, we experimentally show that only a small significant subset of these features is needed to achieve the same classification rates as competing to state-of-the-art methods.

[1]  R. Chellappa Introduction of New Editor-in-Chief , 2005 .

[2]  David G. Stork,et al.  Pattern Classification , 1973 .

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

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

[5]  Takashi Washio,et al.  An Apriori-Based Algorithm for Mining Frequent Substructures from Graph Data , 2000, PKDD.

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

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

[8]  Cordelia Schmid,et al.  Local Features and Kernels for Classification of Texture and Object Categories: A Comprehensive Study , 2006, 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'06).

[9]  M. Fatih Demirci,et al.  Efficient many-to-many feature matching under the l1 norm , 2011, Comput. Vis. Image Underst..

[10]  Masoud Nikravesh,et al.  Feature Extraction: Foundations and Applications (Studies in Fuzziness and Soft Computing) , 2006 .

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

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

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

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

[15]  Larry A. Rendell,et al.  The Feature Selection Problem: Traditional Methods and a New Algorithm , 1992, AAAI.

[16]  M. Fatih Demirci,et al.  Object Recognition as Many-to-Many Feature Matching , 2006, International Journal of Computer Vision.

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

[18]  Edwin R. Hancock,et al.  Graph Characterization via Ihara Coefficients , 2011, IEEE Transactions on Neural Networks.

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

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

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

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

[23]  Ernest Valveny,et al.  Vocabulary Selection for Graph of Words Embedding , 2011, IbPRIA.

[24]  Luc De Raedt,et al.  Feature Construction with Version Spaces for Biochemical Applications , 2001, ICML.

[25]  Robert P. W. Duin,et al.  Prototype selection for dissimilarity-based classifiers , 2006, Pattern Recognit..

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

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

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

[29]  Ernest Valveny,et al.  Graph embedding in vector spaces by node attribute statistics , 2012, Pattern Recognit..

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

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

[32]  Edwin R. Hancock,et al.  A Riemannian approach to graph embedding , 2007, Pattern Recognit..

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

[34]  Ernest Valveny,et al.  Graph of Words Embedding for Molecular Structure-Activity Relationship Analysis , 2010, CIARP.

[35]  Masoud Nikravesh,et al.  Feature Extraction - Foundations and Applications , 2006, Feature Extraction.

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

[37]  A. Atiya,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[38]  Ali Shokoufandeh,et al.  Indexing hierarchical structures using graph spectra , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

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

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

[43]  Ernest Valveny,et al.  Dimensionality Reduction for Graph of Words Embedding , 2011, GbRPR.