Cooperative multi-objective evolutionary support vector machines for multiclass problems

In recent years, evolutionary algorithms have been found to be effective and efficient techniques to train support vector machines (SVMs) for binary classification problems while multiclass problems have been neglected. This paper proposes CMOE-SVM: Cooperative Multi-Objective Evolutionary SVMs for multiclass problems. CMOE-SVM enables SVMs to handle multiclass problems via co-evolutionary optimization, by breaking down the original M-class problem into M simpler ones, which are optimized simultaneously in a cooperative manner. Furthermore, CMOE-SVM can explicitly maximize the margin and reduce the training error (the two components of the SVM optimization), by means of multi-objective optimization. Through a comprehensive experimental evaluation using a suite of benchmark datasets, we validate the performance of CMOE-SVM. The experimental results, supported by statistical tests, give evidence of the effectiveness of the proposed approach for solving multiclass classification problems.

[1]  Francisco Herrera,et al.  MC2ESVM: Multiclass Classification Based on Cooperative Evolution of Support Vector Machines , 2018, IEEE Computational Intelligence Magazine.

[2]  Yi Lin Multicategory Support Vector Machines, Theory, and Application to the Classification of . . . , 2003 .

[3]  Isabelle Guyon,et al.  Comparison of classifier methods: a case study in handwritten digit recognition , 1994, Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3 - Conference C: Signal Processing (Cat. No.94CH3440-5).

[4]  Richard K. Belew,et al.  New Methods for Competitive Coevolution , 1997, Evolutionary Computation.

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

[6]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[7]  Yoshua Bengio,et al.  Random Search for Hyper-Parameter Optimization , 2012, J. Mach. Learn. Res..

[8]  Jason Weston,et al.  Support vector machines for multi-class pattern recognition , 1999, ESANN.

[9]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[10]  Francisco Herrera,et al.  An Evolutionary Multiobjective Model and Instance Selection for Support Vector Machines With Pareto-Based Ensembles , 2017, IEEE Transactions on Evolutionary Computation.

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

[12]  Madson Luiz Dantas Dias,et al.  Evolutionary support vector machines: A dual approach , 2016, CEC.

[13]  Yves Lecourtier,et al.  A multi-model selection framework for unknown and/or evolutive misclassification cost problems , 2010, Pattern Recognit..

[14]  Jesús Alcalá-Fdez,et al.  KEEL Data-Mining Software Tool: Data Set Repository, Integration of Algorithms and Experimental Analysis Framework , 2011, J. Multiple Valued Log. Soft Comput..

[15]  Rudolf Paul Wiegand,et al.  An analysis of cooperative coevolutionary algorithms , 2004 .

[16]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[17]  Ulrich H.-G. Kreßel,et al.  Pairwise classification and support vector machines , 1999 .

[18]  Koby Crammer,et al.  On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines , 2002, J. Mach. Learn. Res..

[19]  Nello Cristianini,et al.  Large Margin DAGs for Multiclass Classification , 1999, NIPS.

[20]  Ingo Mierswa,et al.  Evolutionary learning with kernels: a generic solution for large margin problems , 2006, GECCO '06.

[21]  Chih-Jen Lin,et al.  A comparison of methods for multiclass support vector machines , 2002, IEEE Trans. Neural Networks.

[22]  Francisco Herrera,et al.  Evolutionary wrapper approaches for training set selection as preprocessing mechanism for support vector machines: Experimental evaluation and support vector analysis , 2016, Appl. Soft Comput..

[23]  Kenneth A. De Jong,et al.  Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents , 2000, Evolutionary Computation.

[24]  Jacques Wainer,et al.  Empirical Evaluation of Resampling Procedures for Optimising SVM Hyperparameters , 2017, J. Mach. Learn. Res..

[25]  Yann Guermeur,et al.  MSVMpack: A Multi-Class Support Vector Machine Package , 2011, J. Mach. Learn. Res..

[26]  S. García,et al.  An Extension on "Statistical Comparisons of Classifiers over Multiple Data Sets" for all Pairwise Comparisons , 2008 .

[27]  Gintautas Dzemyda,et al.  Large-Scale Data Analysis Using Heuristic Methods , 2011, Informatica.

[28]  John C. Platt,et al.  Fast training of support vector machines using sequential minimal optimization, advances in kernel methods , 1999 .

[29]  Emmanuel Monfrini,et al.  A Quadratic Loss Multi-Class SVM for which a Radius-Margin Bound Applies , 2011, Informatica.