Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach

Robust linear discriminant analysis (RLDA) methods are becoming the better choice for classification problems as compared to the classical linear discriminant analysis (LDA) due to their ability in circumventing outliers issue. Classical LDA relies on the usual location and scale estimators which ar...

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Main Author:	Melik, Hameedah Naeem
Format:	Thesis
Language:	eng eng
Published:	2017
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	https://etd.uum.edu.my/6810/1/s819154_01.pdf https://etd.uum.edu.my/6810/2/s819154_02.pdf
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id	my-uum-etd.6810
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad
topic	QA273-280 Probabilities Mathematical statistics
spellingShingle	QA273-280 Probabilities Mathematical statistics Melik, Hameedah Naeem Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
description	Robust linear discriminant analysis (RLDA) methods are becoming the better choice for classification problems as compared to the classical linear discriminant analysis (LDA) due to their ability in circumventing outliers issue. Classical LDA relies on the usual location and scale estimators which are the sample mean and covariance matrix. The sensitivity of these estimators towards outliers will jeopardize the classification process. To alleviate the issue, robust estimators of location and covariance are proposed. Thus, in this study, two RLDA for two groups classification were modified using two highly robust location estimators namely Modified One-Step M-estimator (MOM) and Winsorized Modified One-Step M-estimator (WMOM). Integrated with a highly robust scale estimator, Qn, in the trimming criteria of MOM and WMOM, two new RLDA were developed known as RLDAMQ and RLDAWMQ respectively. In the computation of the new RLDA, the usual mean is replaced by MOM-Qn and WMOM-Qn accordingly. The performance of the new RLDA were tested on simulated as well as real data and then compared against the classical LDA. For simulated data, several variables were manipulated to create various conditions that always occur in real life. The variables were homogeneity of covariance (equal and unequal), samples (balanced and unbalanced), dimension of variables, and the percentage of contamination. In general, the results show that the performance of the new RLDA are more favorable than the classical LDA in terms of average misclassification error for contaminated data, although the new RLDA have the shortcoming of requiring more computational time. RLDAMQ works best under balanced sample sizes while RLDAWMQ surpasses the others under unbalanced sample sizes. When real financial data were considered, RLDAMQ shows capability in handling outliers with lowest misclassification error. As a conclusion, this research has achieved its primary objective which is to develop new RLDA for two groups classification of multivariate data in the presence of outliers.
format	Thesis
qualification_name	other
qualification_level	Master's degree
author	Melik, Hameedah Naeem
author_facet	Melik, Hameedah Naeem
author_sort	Melik, Hameedah Naeem
title	Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
title_short	Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
title_full	Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
title_fullStr	Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
title_full_unstemmed	Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach
title_sort	robust linear discriminant analysis using mom-qn and wmom-qn estimators: coordinate-wise approach
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2017
url	https://etd.uum.edu.my/6810/1/s819154_01.pdf https://etd.uum.edu.my/6810/2/s819154_02.pdf
_version_	1747828118203138048
spelling	my-uum-etd.68102021-05-10T06:34:39Z Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach 2017 Melik, Hameedah Naeem Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Robust linear discriminant analysis (RLDA) methods are becoming the better choice for classification problems as compared to the classical linear discriminant analysis (LDA) due to their ability in circumventing outliers issue. Classical LDA relies on the usual location and scale estimators which are the sample mean and covariance matrix. The sensitivity of these estimators towards outliers will jeopardize the classification process. To alleviate the issue, robust estimators of location and covariance are proposed. Thus, in this study, two RLDA for two groups classification were modified using two highly robust location estimators namely Modified One-Step M-estimator (MOM) and Winsorized Modified One-Step M-estimator (WMOM). Integrated with a highly robust scale estimator, Qn, in the trimming criteria of MOM and WMOM, two new RLDA were developed known as RLDAMQ and RLDAWMQ respectively. In the computation of the new RLDA, the usual mean is replaced by MOM-Qn and WMOM-Qn accordingly. The performance of the new RLDA were tested on simulated as well as real data and then compared against the classical LDA. For simulated data, several variables were manipulated to create various conditions that always occur in real life. The variables were homogeneity of covariance (equal and unequal), samples (balanced and unbalanced), dimension of variables, and the percentage of contamination. In general, the results show that the performance of the new RLDA are more favorable than the classical LDA in terms of average misclassification error for contaminated data, although the new RLDA have the shortcoming of requiring more computational time. RLDAMQ works best under balanced sample sizes while RLDAWMQ surpasses the others under unbalanced sample sizes. When real financial data were considered, RLDAMQ shows capability in handling outliers with lowest misclassification error. As a conclusion, this research has achieved its primary objective which is to develop new RLDA for two groups classification of multivariate data in the presence of outliers. 2017 Thesis https://etd.uum.edu.my/6810/ https://etd.uum.edu.my/6810/1/s819154_01.pdf text eng public https://etd.uum.edu.my/6810/2/s819154_02.pdf text eng public other masters Universiti Utara Malaysia Abu-Shawiesh, M. O. A., Banik, S., & Golam Kibria, B. M. (2011). 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