Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations

Multiple kernel learning is a paradigm which employs a properly constructed chain of kernel functions able to simultaneously analyse different data or different representations of the same data. In this paper, we propose an hybrid classification system based on a linear combination of multiple kernels defined over multiple dissimilarity spaces. The core of the training procedure is the joint optimisation of kernel weights and representatives selection in the dissimilarity spaces. This equips the system with a two-fold knowledge discovery phase: by analysing the weights, it is possible to check which representations are more suitable for solving the classification problem, whereas the pivotal patterns selected as representatives can give further insights on the modelled system, possibly with the help of field-experts. The proposed classification system is tested on real proteomic data in order to predict proteins’ functional role starting from their folded structure: specifically, a set of eight representations are drawn from the graph-based protein folded description. The proposed multiple kernel-based system has also been benchmarked against a clustering-based classification system also able to exploit multiple dissimilarities simultaneously. Computational results show remarkable classification capabilities and the knowledge discovery analysis is in line with current biological knowledge, suggesting the reliability of the proposed system.

[1]  Afra Zomorodian,et al.  Fast construction of the Vietoris-Rips complex , 2010, Comput. Graph..

[2]  O. V. Galzitskaya,et al.  Radius of gyration as an indicator of protein structure compactness , 2008, Molecular Biology.

[3]  Alexander J. Smola,et al.  Learning with non-positive kernels , 2004, ICML.

[4]  Antonello Rizzi,et al.  On the Optimization of Embedding Spaces via Information Granulation for Pattern Recognition , 2020, 2020 International Joint Conference on Neural Networks (IJCNN).

[5]  Christian F. A. Negre,et al.  Eigenvector centrality for characterization of protein allosteric pathways , 2017, Proceedings of the National Academy of Sciences.

[6]  Lorenzo Livi,et al.  A new Granular Computing approach for sequences representation and classification , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[7]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[8]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[9]  M. Randic,et al.  On Characterization of 3D Molecular Structure , 2002 .

[10]  Shehroz S. Khan,et al.  A Survey of Recent Trends in One Class Classification , 2009, AICS.

[11]  Antonello Rizzi,et al.  Calibration Techniques for Binary Classification Problems: A Comparative Analysis , 2019, IJCCI.

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

[13]  Antonello Rizzi,et al.  Distance Matrix Pre-Caching and Distributed Computation of Internal Validation Indices in k-medoids Clustering , 2018, 2018 International Joint Conference on Neural Networks (IJCNN).

[14]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[15]  Antonello Rizzi,et al.  Automatic Classification of Graphs by Symbolic Histograms , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[16]  Dong Hoon Lee,et al.  Secure Similarity Search , 2007 .

[17]  Ethem Alpaydin,et al.  Multiple Kernel Learning Algorithms , 2011, J. Mach. Learn. Res..

[18]  Antonello Rizzi,et al.  A cluster-based dissimilarity learning approach for localized fault classification in Smart Grids , 2018, Swarm Evol. Comput..

[19]  I. Gutman,et al.  Laplacian energy of a graph , 2006 .

[20]  L. Pauling,et al.  The structure of proteins; two hydrogen-bonded helical configurations of the polypeptide chain. , 1951, Proceedings of the National Academy of Sciences of the United States of America.

[21]  J. Mercer Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations , 1909 .

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

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

[24]  Alessandro Giuliani,et al.  Toward a Multilevel Representation of Protein Molecules: Comparative Approaches to the Aggregation/Folding Propensity Problem , 2014, Inf. Sci..

[25]  Cathy H. Wu,et al.  UniProt: the Universal Protein knowledgebase , 2004, Nucleic Acids Res..

[26]  Alessandro Giuliani,et al.  Analysis of heat kernel highlights the strongly modular and heat-preserving structure of proteins , 2014, 1409.1819.

[27]  Alessandro Giuliani,et al.  A generative model for protein contact networks , 2015, Journal of biomolecular structure & dynamics.

[28]  Yiyu Yao,et al.  Granular Computing , 2008 .

[29]  Thomas M. Cover,et al.  Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition , 1965, IEEE Trans. Electron. Comput..

[30]  Lorenzo Livi,et al.  Modeling and recognition of smart grid faults by a combined approach of dissimilarity learning and one-class classification , 2014, Neurocomputing.

[31]  Sebastiano Vigna,et al.  Axioms for Centrality , 2013, Internet Math..

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

[33]  Klaus-Robert Müller,et al.  Feature Discovery in Non-Metric Pairwise Data , 2004, J. Mach. Learn. Res..

[34]  Maya R. Gupta,et al.  Learning kernels from indefinite similarities , 2009, ICML '09.

[35]  L. Zadeh,et al.  Data mining, rough sets and granular computing , 2002 .

[36]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[37]  S. Butler Algebraic aspects of the normalized Laplacian , 2016 .

[38]  Robert Ghrist,et al.  Elementary Applied Topology , 2014 .

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

[40]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[41]  Lena Jaeger,et al.  Introduction To Protein Structure , 2016 .

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

[43]  Valeria Simoncini,et al.  Basic Statistical Concepts , 2010 .

[44]  Mark Newman,et al.  Networks: An Introduction , 2010 .

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

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

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

[48]  J. Hausmann On the Vietoris-Rips complexes and a Cohomology Theory for metric spaces , 1996 .

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

[50]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[51]  E. Webb Enzyme nomenclature 1992. Recommendations of the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology on the Nomenclature and Classification of Enzymes. , 1992 .

[52]  David M. W. Powers,et al.  Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation , 2011, ArXiv.

[53]  Edwin R. Hancock,et al.  Graph Clustering Using Heat Content Invariants , 2005, IbPRIA.

[54]  Mehryar Mohri,et al.  Learning Non-Linear Combinations of Kernels , 2009, NIPS.

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

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

[57]  A. Giuliani,et al.  Protein contact networks: an emerging paradigm in chemistry. , 2013, Chemical reviews.

[58]  Nello Cristianini,et al.  Learning the Kernel Matrix with Semidefinite Programming , 2002, J. Mach. Learn. Res..

[59]  Maya R. Gupta,et al.  Similarity-based Classification: Concepts and Algorithms , 2009, J. Mach. Learn. Res..

[60]  Alessandro Giuliani,et al.  Multifractal characterization of protein contact networks , 2014, 1410.0890.

[61]  Sergio Barbarossa,et al.  Topological Signal Processing Over Simplicial Complexes , 2019, IEEE Transactions on Signal Processing.

[62]  S. Wuchty Scale-free behavior in protein domain networks. , 2001, Molecular biology and evolution.

[63]  Boonserm Kijsirikul,et al.  Evolving Hyperparameters of Support Vector Machines Based on Multi-Scale RBF Kernels , 2006, Intelligent Information Processing.

[64]  Ethem Alpaydin,et al.  Localized multiple kernel learning , 2008, ICML '08.

[65]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[66]  Travis E. Oliphant,et al.  Python for Scientific Computing , 2007, Computing in Science & Engineering.

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

[68]  Alessandro Giuliani,et al.  Protein contact network topology: a natural language for allostery. , 2015, Current opinion in structural biology.

[69]  Lorenzo Livi,et al.  Optimized dissimilarity space embedding for labeled graphs , 2014, Inf. Sci..

[70]  Antonello Rizzi,et al.  Supervised Approaches for Protein Function Prediction by Topological Data Analysis , 2018, 2018 International Joint Conference on Neural Networks (IJCNN).

[71]  D. F. Marks,et al.  An introduction , 1988, Experientia.

[72]  Danijela Horak,et al.  Persistent homology of complex networks , 2008, 0811.2203.

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

[74]  Michael I. Jordan,et al.  Multiple kernel learning, conic duality, and the SMO algorithm , 2004, ICML.

[75]  H. Edelsbrunner,et al.  Topological data analysis , 2011 .

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

[77]  D. W. Scott On optimal and data based histograms , 1979 .

[78]  Alessandro Giuliani,et al.  Characterization of Graphs for Protein Structure Modeling and Recognition of Solubility , 2014, ArXiv.

[79]  Gunnar Rätsch,et al.  Large Scale Multiple Kernel Learning , 2006, J. Mach. Learn. Res..

[80]  Bartek Wilczynski,et al.  Biopython: freely available Python tools for computational molecular biology and bioinformatics , 2009, Bioinform..

[81]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[82]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[83]  Julio Saez-Rodriguez,et al.  BioServices: a common Python package to access biological Web Services programmatically , 2013, Bioinform..

[84]  P W DuinRobert,et al.  The dissimilarity space , 2012 .

[85]  Antonello Rizzi,et al.  Efficient Approaches for Solving the Large-Scale k-medoids Problem , 2017, IJCCI.

[86]  Sebastian Raschka,et al.  BioPandas: Working with molecular structures in pandas DataFrames , 2017, J. Open Source Softw..

[87]  Enys Mones,et al.  Hierarchy Measure for Complex Networks , 2012, PloS one.

[88]  Yiqiang Chen,et al.  Building Sparse Multiple-Kernel SVM Classifiers , 2009, IEEE Transactions on Neural Networks.

[89]  Amir Hussain,et al.  A novel multi-modal machine learning based approach for automatic classification of EEG recordings in dementia , 2019, Neural Networks.

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

[91]  Robert P. W. Duin,et al.  The dissimilarity space: Bridging structural and statistical pattern recognition , 2012, Pattern Recognit. Lett..

[92]  Antonello Rizzi,et al.  Online Handwriting Recognition by the Symbolic Histograms Approach , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[93]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[94]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[95]  Prem Kumar Singh,et al.  Similar Vague Concepts Selection Using Their Euclidean Distance at Different Granulation , 2018, Cognitive Computation.

[96]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[97]  Delmiro Fernandez-Reyes,et al.  Adapting multiple kernel parameters for support vector machines using genetic algorithms , 2005, 2005 IEEE Congress on Evolutionary Computation.

[98]  Alessandro Giuliani,et al.  Spectral reconstruction of protein contact networks , 2017 .

[99]  Alessandro Giuliani,et al.  Supervised Approaches for Function Prediction of Proteins Contact Networks from Topological Structure Information , 2017, SCIA.

[100]  Horst Bunke,et al.  On a relation between graph edit distance and maximum common subgraph , 1997, Pattern Recognit. Lett..

[101]  Enrico Guarnera,et al.  Allosteric sites: remote control in regulation of protein activity. , 2016, Current opinion in structural biology.

[102]  Muhammad Abdul Qadir,et al.  Semantic Inconsistency Errors in Ontology , 2007 .

[103]  Ulrik Brandes,et al.  On variants of shortest-path betweenness centrality and their generic computation , 2008, Soc. Networks.

[104]  Afra Zomorodian,et al.  Computing Persistent Homology , 2004, SCG '04.

[105]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[106]  J. A. Rodríguez-Velázquez,et al.  Complex Networks as Hypergraphs , 2005, physics/0505137.

[107]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[109]  Antonello Rizzi,et al.  Dissimilarity Space Representations and Automatic Feature Selection for Protein Function Prediction , 2018, 2018 International Joint Conference on Neural Networks (IJCNN).

[110]  Antonello Rizzi,et al.  Evolutionary Optimization of an Affine Model for Vulnerability Characterization in Smart Grids , 2018, 2018 International Joint Conference on Neural Networks (IJCNN).

[111]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

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

[114]  W. Youden,et al.  Index for rating diagnostic tests , 1950, Cancer.

[115]  Mikko Kivelä,et al.  Generalizations of the clustering coefficient to weighted complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[116]  Edwin R. Hancock,et al.  Graph characteristics from the heat kernel trace , 2009, Pattern Recognit..

[117]  Alfredo Colosimo,et al.  Nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. , 2002, Chemical reviews.

[118]  Masaru Tomita,et al.  Proteins as networks: usefulness of graph theory in protein science. , 2008, Current protein & peptide science.

[119]  Paul D. Minton,et al.  Statistics: The Exploration and Analysis of Data , 2002, Technometrics.

[120]  William Stafford Noble,et al.  Nonstationary kernel combination , 2006, ICML.

[121]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[122]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[123]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[124]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[125]  David A. Clifton,et al.  A review of novelty detection , 2014, Signal Process..

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

[127]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[128]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[129]  Antonello Rizzi,et al.  Efficient Approaches for Solving the Large-Scale k-Medoids Problem: Towards Structured Data , 2017, IJCCI.

[130]  J. Mendel Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.