Exploiting Cliques for Granular Computing-based Graph Classification

The most fascinating aspect of graphs is their ability to encode the information contained in the inner structural organization between its constituting elements. Learning from graphs belong to the so-called Structural Pattern Recognition, from which Graph Embedding emerged as a successful method for processing graphs by evaluating their dissimilarity in a suitable geometric space. In this paper, we investigate the possibility to perform the embedding into a geometric space by leveraging to peculiar constituent graph substructures extracted from training set, namely the maximal cliques, and providing the performances obtained under three main aspects concerning classification capabilities, running times and model complexity. Thanks to a Granular Computing approach, the employed methodology can be seen as a powerful framework able to synthesize models suitable to be interpreted by field-experts, pushing the boundary towards new frontiers in the field of explainable AI and knowledge discovery also in big data contexts.

[1]  Rong Yang,et al.  Machine Learning and Data Mining in Pattern Recognition , 2012, Lecture Notes in Computer Science.

[2]  Andrzej Bargiela,et al.  The roots of granular computing , 2006, 2006 IEEE International Conference on Granular Computing.

[3]  Alessio Micheli,et al.  Neural Network for Graphs: A Contextual Constructive Approach , 2009, IEEE Transactions on Neural Networks.

[4]  Jure Leskovec,et al.  Supervised random walks: predicting and recommending links in social networks , 2010, WSDM '11.

[5]  A. Giuliani,et al.  Granular Computing Techniques for Bioinformatics Pattern Recognition Problems in Non-metric Spaces , 2018 .

[6]  R. Luce,et al.  A method of matrix analysis of group structure , 1949, Psychometrika.

[7]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[8]  Lorenzo Livi,et al.  A Granular Computing approach to the design of optimized graph classification systems , 2014, Soft Comput..

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

[10]  Simone Scardapane,et al.  An interpretable graph-based image classifier , 2014, 2014 International Joint Conference on Neural Networks (IJCNN).

[11]  Kurt Mehlhorn,et al.  Weisfeiler-Lehman Graph Kernels , 2011, J. Mach. Learn. Res..

[12]  Jure Leskovec,et al.  How Powerful are Graph Neural Networks? , 2018, ICLR.

[13]  Jimmy J. Lin,et al.  WTF: the who to follow service at Twitter , 2013, WWW.

[14]  C. Bron,et al.  Algorithm 457: finding all cliques of an undirected graph , 1973 .

[15]  Simone Scardapane,et al.  Granular Computing Techniques for Classification and Semantic Characterization of Structured Data , 2015, Cognitive Computation.

[16]  Anthony Widjaja,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2003, IEEE Transactions on Neural Networks.

[17]  J. Moon,et al.  On cliques in graphs , 1965 .

[18]  Davide Bacciu,et al.  Contextual Graph Markov Model: A Deep and Generative Approach to Graph Processing , 2018, ICML.

[19]  Alessandro Giuliani,et al.  Metabolic networks classification and knowledge discovery by information granulation , 2019, Comput. Biol. Chem..

[20]  Xiao Bai,et al.  Graph-Based Methods in Computer Vision: Developments and Applications , 2012 .

[21]  Alessandro Sperduti,et al.  Universal Readout for Graph Convolutional Neural Networks , 2019, 2019 International Joint Conference on Neural Networks (IJCNN).

[22]  Claudio Gallicchio,et al.  Graph Echo State Networks , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[23]  Alessandro Sperduti,et al.  Ordered Decompositional DAG kernels enhancements , 2015, Neurocomputing.

[24]  Neil Salkind,et al.  Encyclopedia of educational psychology , 2008 .

[25]  Alessandro Giuliani,et al.  Why network approach can promote a new way of thinking in biology , 2014, Front. Genet..

[26]  Rayleigh.  The Problem of the Random Walk , 1905, Nature.

[27]  Horst Bunke,et al.  Graph-Based Tools for Data Mining and Machine Learning , 2003, MLDM.

[28]  Alessandro Giuliani,et al.  Protein–Protein Interactions: The Structural Foundation of Life Complexity , 2017 .

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

[30]  Tom A. B. Snijders,et al.  Social Network Analysis , 2011, International Encyclopedia of Statistical Science.

[31]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[32]  Kaspar Riesen,et al.  Graph Classification by Means of Lipschitz Embedding , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[34]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

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

[36]  Noel M. Tichy,et al.  An Analysis of Clique Formation and Structure in Organizations. , 1973 .

[37]  Tsau Young Lin,et al.  Granular Computing , 2003, RSFDGrC.

[38]  Antonello Rizzi,et al.  Stochastic Information Granules Extraction for Graph Embedding and Classification , 2019, IJCCI.

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

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

[41]  Dimitri Van De Ville,et al.  Machine Learning with Brain Graphs: Predictive Modeling Approaches for Functional Imaging in Systems Neuroscience , 2013, IEEE Signal Processing Magazine.

[42]  Horst Bunke,et al.  Towards Bridging the Gap between Statistical and Structural Pattern Recognition: Two New Concepts in Graph Matching , 2001, ICAPR.

[43]  Antonello Rizzi,et al.  A Novel Algorithm for Online Inexact String Matching and its FPGA Implementation , 2017, Cognitive Computation.

[44]  Alessandro Giuliani,et al.  (Hyper)Graph Embedding and Classification via Simplicial Complexes , 2019, Algorithms.