An Efficient Estimation and Classification Methods for High Dimensional Data Using Robust Iteratively Reweighted SIMPLS Algorithm Based on <i>nu</i>-Support Vector Regression

Rashid, Abdullah Mohammed; Midi, Habshah; Slwabi, Waleed Dhhan; Arasan, Jayanthi

doi:10.1109/access.2021.3066172

Cited by 6 publications

(11 citation statements)

References 31 publications

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“…Leverage points can be classified into good (GLP) and bad leverage points (BLP). Unlike BLPs, GLPs follow the pattern of the majority of the data; hence they are not considered as IOs as they have little or no influence on the calculated values of numerous estimates [2,3]. In this connection, Rashid et al [2] stated that IOs could be vertical outliers (VO) or BLPs.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike BLPs, GLPs follow the pattern of the majority of the data; hence they are not considered as IOs as they have little or no influence on the calculated values of numerous estimates [2,3]. In this connection, Rashid et al [2] stated that IOs could be vertical outliers (VO) or BLPs. Thus, it is very crucial to identify IOs as they are responsible for the misleading conclusion about the fitted regression model and various estimates.…”

Section: Introductionmentioning

confidence: 99%

“…The main objective of this study are: (1) to represent the leverage values of hat matrix of linear regression to GSM model; (2) to extend the ISR of linear regression to GSM model;…”

Section: Introductionmentioning

confidence: 99%

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Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Baba¹,

Midi²,

Adam³

et al. 2021

Preprint

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Influential Observations, which are outliers in x direction, y direction or both, remain a hitch in classical regression model fitting. Spatial regression model, with peculiar nature of outliers due to their local nature, is not free from the effect of such influential observations. Researchers have adapted some classical regression techniques to the spatial models and yielded satisfactory results. However, masking or/and swamping remain stumbling block to such methods. We obtained the spatial representation of the classical regression measures of diagnostic in general spatial model. Commonly used diagnostic measure in spatial diagnostic, the Cook's distance, is compared to some robust methods, Hi2 (using robust and non-robust measures), and classification based on generalized residuals and diagnostic generalized potentials, ISRs-Posi and ESRs-Posi, with the help of the obtained spatial prediction residuals and the spatial leverage term. Results of simulation and applications to real data have shown the advantage of the ISRs-Posi and ESRs-Posi due to classification of outliers over Cook's distance and non-robust Hsi12, which suffer from masking, and robust Hsi22 which suffer from swamping in general spatial model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Baba¹,

Midi²,

Adam³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Leverage points can be classified into good (GLPs) and bad leverage points (BLPs). Unlike BLPs, GLPs follow the pattern of the majority of the data; hence, they are not considered as IOs as they have little or no influence on the calculated values of numerous estimates [2,3]. In this connection, Rashid et al [2] stated that IOs could be vertical outliers (VO) or BLPs.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike BLPs, GLPs follow the pattern of the majority of the data; hence, they are not considered as IOs as they have little or no influence on the calculated values of numerous estimates [2,3]. In this connection, Rashid et al [2] stated that IOs could be vertical outliers (VO) or BLPs. Thus, it is very crucial to identify IOs as they are responsible for misleading conclusions about the fitted regression models and various other estimates.…”

Section: Introductionmentioning

confidence: 99%

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

et al. 2021

Self Cite

View full text Add to dashboard Cite

Influential observations (IOs), which are outliers in the x direction, y direction or both, remain a problem in the classical regression model fitting. Spatial regression models have a peculiar kind of outliers because they are local in nature. Spatial regression models are also not free from the effect of influential observations. Researchers have adapted some classical regression techniques to spatial models and obtained satisfactory results. However, masking or/and swamping remains a stumbling block for such methods. In this article, we obtain a measure of spatial Studentized prediction residuals that incorporate spatial information on the dependent variable and the residuals. We propose a robust spatial diagnostic plot to classify observations into regular observations, vertical outliers, good and bad leverage points using a classification based on spatial Studentized prediction residuals and spatial diagnostic potentials, which we refer to as ISRs−Posi and ESRs−Posi. Observations that fall into the vertical outliers and bad leverage points categories are referred to as IOs. Representations of some classical regression measures of diagnostic in general spatial models are presented. The commonly used diagnostic measure in spatial diagnostics, the Cook’s distance, is compared to some robust methods, Hi2 (using robust and non-robust measures), and our proposed ISRs−Posi and ESRs−Posi plots. Results of our simulation study and applications to real data showed that the Cook’s distance, non-robust Hsi12 and robust Hsi22 were not very successful in detecting IOs. The Hsi12 suffered from the masking effect, and the robust Hsi22 suffered from swamping in general spatial models. Interestingly, the results showed that the proposed ESRs−Posi plot, followed by the ISRs−Posi plot, was very successful in classifying observations into the correct groups, hence correctly detecting the real IOs.

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Partial least median of squares regression

Xie

Feng

Liu

et al. 2022

Journal of Chemometrics

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In modern data analysis, there is an increasing availability of datasets with numerous variables. Linear models that deal with abundant predictor variables often have poor performance because they tend to produce large variances. As well known, partial least squares (PLS) regression standouts because it is serviceable even if the number of variables far exceeds the number of samples. However, PLS, at its core, is a least‐squares method based on latent space, which is spanned by the components extracted from the original predictors. Hence, it is sensitive to outliers. In this study, incorporating the idea of least median of squares, we propose a new robust PLS method, namely, partial least median of squares (PLMS) regression. Unlike most of the robust counterparts, we solve the PLMS problem via modern optimization rather than a heuristic process or a reweighting strategy. A classical PLS method and two of the most efficient robust PLS methods are compared with our method. Results on simulations and two real‐world data sets demonstrate the effectiveness and robustness of our approach.

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An Efficient Estimation and Classification Methods for High Dimensional Data Using Robust Iteratively Reweighted SIMPLS Algorithm Based on nu-Support Vector Regression

Cited by 6 publications

References 31 publications

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Partial least median of squares regression

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