An Ensemble of Kernel Ridge Regression for Multi-class Classification

Abstract We propose an ensemble of kernel ridge regression based classifiers in this paper. Kernel ridge regression admits a closed form solution making it faster to compute and also making it suitable to use for ensemble methods for small and medium sized data sets. Our method uses random vector functional link network to generate training samples for kernel ridge regression classifiers. Several kernel ridge regression classifiers are constructed from different training subsets in each base classifier. The partitioning of the training samples into different subsets leads to a reduction in computational complexity when calculating matrix inverse compared with the standard approach of using all N samples for kernel matrix inversion. The proposed method is evaluated using well known multi-class UCI data sets. Experimental results show the proposed ensemble method outperforms the single kernel ridge regression classifier and its bagging version.

[1]  Lior Rokach,et al.  Ensemble-based classifiers , 2010, Artificial Intelligence Review.

[2]  P. N. Suganthan,et al.  A comprehensive evaluation of random vector functional link networks , 2016, Inf. Sci..

[3]  Petros Drineas,et al.  On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning , 2005, J. Mach. Learn. Res..

[4]  Sung-Bae Cho,et al.  A comprehensive survey on functional link neural networks and an adaptive PSO–BP learning for CFLNN , 2010, Neural Computing and Applications.

[5]  Ponnuthurai N. Suganthan,et al.  Instance based random forest with rotated feature space , 2013, 2013 IEEE Symposium on Computational Intelligence and Ensemble Learning (CIEL).

[6]  B. Rosenberg Human Swarms , a real-time paradigm for Collective Intelligence , 2015 .

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

[8]  Dejan J. Sobajic,et al.  Neural-net computing and the intelligent control of systems , 1992 .

[9]  Alexander Gammerman,et al.  Ridge Regression Learning Algorithm in Dual Variables , 1998, ICML.

[10]  Svetha Venkatesh,et al.  Face Recognition Using Kernel Ridge Regression , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[12]  Ponnuthurai N. Suganthan,et al.  Oblique Decision Tree Ensemble via Multisurface Proximal Support Vector Machine , 2015, IEEE Transactions on Cybernetics.

[13]  Ponnuthurai N. Suganthan,et al.  Random vector functional link network for short-term electricity load demand forecasting , 2016, Inf. Sci..

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

[15]  Senén Barro,et al.  Do we need hundreds of classifiers to solve real world classification problems? , 2014, J. Mach. Learn. Res..

[16]  Giorgio Valentini,et al.  Ensembles of Learning Machines , 2002, WIRN.

[17]  Ponnuthurai N. Suganthan,et al.  Towards generating random forests via extremely randomized trees , 2014, 2014 International Joint Conference on Neural Networks (IJCNN).

[18]  Ron Kohavi,et al.  Bias Plus Variance Decomposition for Zero-One Loss Functions , 1996, ICML.

[19]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[20]  Yoav Freund,et al.  Boosting the margin: A new explanation for the effectiveness of voting methods , 1997, ICML.

[21]  Yoav Freund,et al.  Boosting a weak learning algorithm by majority , 1990, COLT '90.

[22]  R. E. Lee,et al.  Distribution-free multiple comparisons between successive treatments , 1995 .

[23]  Michael Vitale,et al.  The Wisdom of Crowds , 2015, Cell.