Abstract
Kernel logistic regression (KLR) is a powerful nonlinear classifier. The combination of KLR and the truncated-regularized iteratively re-weighted least-squares (TR-IRLS) algorithm, has led to a powerful classification method using small-to-medium size data sets. This method (algorithm), is called truncated-regularized kernel logistic regression (TR-KLR). Compared to support vector machines (SVM) and TR-IRLS on twelve benchmark publicly available data sets, the proposed TR-KLR algorithm is as accurate as, and much faster than, SVM and more accurate than TR-IRLS. The TR-KLR algorithm also has the advantage of providing direct prediction probabilities.
Similar content being viewed by others
References
Asuncion A, Newman DJ (2007) UCI machine learning repository. University of california, irvine, School of information and computer sciences. http://www.ics.uci.edu/~mlearn/MLRepository.html
Canu S, Smola A (2006) Kernel methods and the exponential family. Neurocomputing 69(7–9): 714–720
Chang CC, Lin CJ (2001) LIBSVM: a library for support vector machines. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, London
Garthwaite P, Jolliffe I, Jones B (2002) Statistical inference. Oxford University Press, London
Gunn SR (1998) MATLAB support vector machine toolbox. Software available at http://www.isis.ecs.soton.ac.uk/isystems/kernel/
Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning. Springer, Berlin
Hosmer DW, Lemeshow S (2000) Applied logistic regression, 2nd edn. Wiley, London
Jaakkola TS, Haussler D (1999) Probabilistic kernel regression models. In: Proceedings of the 1999 conference on AI and statistics. Morgan Kaufmann, Cambridge
Karsmakers P, Pelckmans K, Suykens JAK (2007) Multi-class kernel logistic regression: a fixed-size implementation. In: IJCNN: Proceedings of the international joint conference on neural networks, IEEE, pp 1756–1761
Keerthi SS, Duan KB, Shevade SK, Poo AN (2005) A fast dual algorithm for kernel logistic regression. J Mach Learning 61(1–3): 151–165. doi:10.1007/s10994-005-0768-5
Kressel UHG (1999) Pairwise classification and support vector machines. In: Advances in kernel methods: support vector learning. MIT Press, Cambridge, pp 255–268
Komarek P, Moore A (2005) Making LR a core data mining tool with TR-IRLS. In: ICDM: proceedings of the fifth IEEE international conference on data mining, IEEE Computer Society, Washington, USA, pp 685–688
Koh K, Kim S, Boyd S (2007) An interior-point method for large-scale ℓ1-regularized logistic regression. J Mach Learn Res 8: 1519–1555
Komarek P, Moore A (2005) Making logistic regression a core data mining tool: a practical investigation of accuracy, speed, and simplicity. Tech. Rep. CMU-RI-TR-05-27, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA
Lin CJ, Weng RC, Keerthi SS (2007) Trust region newton methods for large-scale logistic regression. In: ICML ’07 proceedings of the 24th international conference on machine learning, ACM, New York, pp 561–568
Malouf R (2002) A comparison of algorithms for maximum entropy parameter estimation. In: COLING-02 proceeding of the 6th conference on natural language learning. Association for Computational Linguistics, Morristown, USA, pp 1–7. doi:10.3115/1118853.1118871
Maalouf M, Trafalis TB (2011) Robust weighted kernel logistic regression in imbalanced and rare events data. Comput Stat Data Anal 55(1): 168–183
Minka TP (2003) A comparison of numerical optimizers for logistic regression. Tech rep, Deptartment of Statistics, Carnegie Mellon University
Platt JC, Cristianini N, Shawe-taylor J (2000) Large margin DAGs for multiclass classification. In: Advances in neural information processing systems, MIT Press, Cambridge, pp 547–553
Rifkin R, Klautau A (2004) In defense of one-vs-all classification. J Mach Learning Res 5: 101–141
Roth V (2001) Probabilistic discriminative kernel classifiers for multi-class problems. In: Proceedings of the 23rd DAGM-symposium on pattern recognition. Springer, London, pp 246–253
Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, London
Vapnik V (1995) The Nature of Statistical Learning. Springer, New York
Zhu J, Hastie T (2005) Kernel logistic regression and the import vector machine. J Comput Graphic Stat 14: 185–205
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Maalouf, M., Trafalis, T.B. & Adrianto, I. Kernel logistic regression using truncated Newton method. Comput Manag Sci 8, 415–428 (2011). https://doi.org/10.1007/s10287-010-0128-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10287-010-0128-1