Logistic Regression Methods with Truncated Newton Method

Considering two-class classification, this paper aims to perform further study on the success of Truncated Newton method in Truncated Regularized Kernel Logistic Regression (TR-KLR) and Iterative Re-weighted Least Square (TR-IRLS) on solving the numerical problem of KLR and RLR. The study was conduc...

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Main Authors:	Jasni, Mohamad Zain, Abdullah, Embong, Rahayu, Santi Puteri, Juwari, S, Purnami, Santi Wulan
Format:	Article
Language:	English
Published:	Elsevier 2012
Subjects:	QA75 Electronic computers. Computer science
Online Access:	http://umpir.ump.edu.my/id/eprint/6189/ http://umpir.ump.edu.my/id/eprint/6189/ http://umpir.ump.edu.my/id/eprint/6189/1/pbmsk-2012-jasni-Logistic_regression_methods_abs_only.pdf

id	ump-6189
recordtype	eprints
spelling	ump-61892018-05-02T06:57:23Z http://umpir.ump.edu.my/id/eprint/6189/ Logistic Regression Methods with Truncated Newton Method Jasni, Mohamad Zain Abdullah, Embong Rahayu, Santi Puteri Juwari, S Purnami, Santi Wulan QA75 Electronic computers. Computer science Considering two-class classification, this paper aims to perform further study on the success of Truncated Newton method in Truncated Regularized Kernel Logistic Regression (TR-KLR) and Iterative Re-weighted Least Square (TR-IRLS) on solving the numerical problem of KLR and RLR. The study was conducted by developing the Newton version of TR-KLR and TR-IRLS algorithm respectively. They are general classifiers which are termed respectively as proposed Newton TR-KLR (NTR-KLR) and proposed NTR Regularized Logistic Regression (NTR-LR). Instead of using IRLS procedure as used by TR-KLR and TR-IRLS, the proposed algorithms implement Newton-Raphson method as the outer algorithm of Truncated Newton for KLR and RLR respectively. Since, for KLR and RLR, IRLS is equivalent to Newton-Raphson method, both proposed algorithms can be expected to perform as well as TR-KLR and TR-IRLS. Moreover, both proposed algorithms are mathematically simpler, because they do not need to restate the Newton-Raphson method as the IRLS procedure before such as in TR-KLR and TR-IRLS. Hence, they simply can be applied as further explanation to the effectiveness of Truncated Newton method in TR-KLR and TR-IRLS respectively. Numerical experiment with Image Segmentation data set has demonstrated that proposed NTR-KLR performs effectively when exist the singularity and the training time problem in using Newton-Raphson method for KLR (KLR-NR). While proposed NTR-LR has performed better training time than RLR with Newton-Raphson (RLR-NR) method on Letter Image data set. Moreover, both proposed algorithms have showed consistency with the convergence theory and have promising results, i.e. accurate and stable classification, on image data sets respectively. Elsevier 2012 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/6189/1/pbmsk-2012-jasni-Logistic_regression_methods_abs_only.pdf Jasni, Mohamad Zain and Abdullah, Embong and Rahayu, Santi Puteri and Juwari, S and Purnami, Santi Wulan (2012) Logistic Regression Methods with Truncated Newton Method. Procedia Engineering, 50. pp. 827-836. ISSN 1877-7058 DOI:10.1016/j.proeng.2012.10.091
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English
topic	QA75 Electronic computers. Computer science
spellingShingle	QA75 Electronic computers. Computer science Jasni, Mohamad Zain Abdullah, Embong Rahayu, Santi Puteri Juwari, S Purnami, Santi Wulan Logistic Regression Methods with Truncated Newton Method
description	Considering two-class classification, this paper aims to perform further study on the success of Truncated Newton method in Truncated Regularized Kernel Logistic Regression (TR-KLR) and Iterative Re-weighted Least Square (TR-IRLS) on solving the numerical problem of KLR and RLR. The study was conducted by developing the Newton version of TR-KLR and TR-IRLS algorithm respectively. They are general classifiers which are termed respectively as proposed Newton TR-KLR (NTR-KLR) and proposed NTR Regularized Logistic Regression (NTR-LR). Instead of using IRLS procedure as used by TR-KLR and TR-IRLS, the proposed algorithms implement Newton-Raphson method as the outer algorithm of Truncated Newton for KLR and RLR respectively. Since, for KLR and RLR, IRLS is equivalent to Newton-Raphson method, both proposed algorithms can be expected to perform as well as TR-KLR and TR-IRLS. Moreover, both proposed algorithms are mathematically simpler, because they do not need to restate the Newton-Raphson method as the IRLS procedure before such as in TR-KLR and TR-IRLS. Hence, they simply can be applied as further explanation to the effectiveness of Truncated Newton method in TR-KLR and TR-IRLS respectively. Numerical experiment with Image Segmentation data set has demonstrated that proposed NTR-KLR performs effectively when exist the singularity and the training time problem in using Newton-Raphson method for KLR (KLR-NR). While proposed NTR-LR has performed better training time than RLR with Newton-Raphson (RLR-NR) method on Letter Image data set. Moreover, both proposed algorithms have showed consistency with the convergence theory and have promising results, i.e. accurate and stable classification, on image data sets respectively.
format	Article
author	Jasni, Mohamad Zain Abdullah, Embong Rahayu, Santi Puteri Juwari, S Purnami, Santi Wulan
author_facet	Jasni, Mohamad Zain Abdullah, Embong Rahayu, Santi Puteri Juwari, S Purnami, Santi Wulan
author_sort	Jasni, Mohamad Zain
title	Logistic Regression Methods with Truncated Newton Method
title_short	Logistic Regression Methods with Truncated Newton Method
title_full	Logistic Regression Methods with Truncated Newton Method
title_fullStr	Logistic Regression Methods with Truncated Newton Method
title_full_unstemmed	Logistic Regression Methods with Truncated Newton Method
title_sort	logistic regression methods with truncated newton method
publisher	Elsevier
publishDate	2012
url	http://umpir.ump.edu.my/id/eprint/6189/ http://umpir.ump.edu.my/id/eprint/6189/ http://umpir.ump.edu.my/id/eprint/6189/1/pbmsk-2012-jasni-Logistic_regression_methods_abs_only.pdf
first_indexed	2023-09-18T22:01:45Z
last_indexed	2023-09-18T22:01:45Z
_version_	1777414445030440960

Logistic Regression Methods with Truncated Newton Method

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