Mathematics and Statistics Vol. 8(5), pp. 493 - 505
DOI: 10.13189/ms.2020.080502
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A Modified Robust Support Vector Regression Approach for Data Containing High Leverage Points and Outliers in the Y-direction

Habshah Midi ¹, Jama Mohamed ^2,*
1 Faculty of Science and Institute for Mathematical Research, University Putra Malaysia, Malaysia
² Faculty of Mathematics and Statistics, College of Applied and Natural Science, University of Hargeisa, Somaliland

ABSTRACT

The support vector regression (SVR) model is currently a very popular non-parametric method used for estimating linear and non-linear relationships between response and predictor variables. However, there is a possibility of selecting vertical outliers as support vectors that can unduly affect the estimates of regression. Outliers from abnormal data points may result in bad predictions. In addition, when both vertical outliers and high leverage points are present in the data, the problem is further complicated. In this paper, we introduced a modified robust SVR technique in the simultaneous presence of these two problems. Three types of SVR models, i.e. eps-regression (ε-SVR), nu-regression (v-SVR) and bound constraint eps-regression (ε-BSVR), with eight different kernel functions are integrated into the new proposed algorithm. Based on 10-fold cross-validation and some model performance measures, the best model with a suitable kernel function is selected. To make the selected model robust, we developed a new double SVR (DSVR) technique based on fixed parameters. This can be used to detect and reduce the weight of influential observations or anomalous points in the data set. The effectiveness of the proposed technique is verified by using a simulation study and some well-known contaminated data sets.

KEYWORDS
Double Support Vector Regression, Fixed Parameters, Vertical Outliers, High Leverage Points, Robust Mahalanobis Distance

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Habshah Midi , Jama Mohamed , "A Modified Robust Support Vector Regression Approach for Data Containing High Leverage Points and Outliers in the Y-direction," Mathematics and Statistics, Vol. 8, No. 5, pp. 493 - 505, 2020. DOI: 10.13189/ms.2020.080502.

(b). APA Format:
Habshah Midi , Jama Mohamed (2020). A Modified Robust Support Vector Regression Approach for Data Containing High Leverage Points and Outliers in the Y-direction. Mathematics and Statistics, 8(5), 493 - 505. DOI: 10.13189/ms.2020.080502.