The single-index support vector regression model to address the problem of high dimensionality |
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Authors: | Waleed Dhhan Sohel Rana Taha Alshaybawee Habshah Midi |
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Institution: | 1. Department of Mathematics, Faculty of Science/Institute for Mathematical Research, University Putra Malaysia, UPM, Serdang Selangor, Malaysia;2. Scientific Research Centre, Nawroz University (NZU), Duhok, Iraq;3. Babylon Municipalities, Ministry of Municipalities and Public Works, Babylon, Iraqw.dhhan@gmail.com;5. Department of Applied Statistics, East West University, Dhaka, Bangladesh;6. Department of Statistics, The University of Al-Qadisiyah, Al Diwaniyah, Iraq |
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Abstract: | ABSTRACTThe last few years, the applications of Support Vector Machine (SVM) for solving classification and regression problems have been increasing, due to its high performance and ability to transform the non-linear relationships among variables to linear form by employing the kernel idea (kernel function). In this work, we develop a semi-parametric approach to fit single-index models to deal with high-dimensional problems. To achieve this goal, we use support vector regression (SVR) for estimating the unknown nonparametric link function, while the single-index is determined by using the semi-parametric least squares method (Ichimura 1993). This development enhances the ability of SVR to solve high-dimensional problem. We design a three simulation examples with high-dimensional problems (linear and nonlinear). The simulations demonstrate the superior performance of the proposed method versus the standard SVR method. This is further illustrated by applying the real data. |
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Keywords: | Single-index model High-dimensional Dimension reduction Sparsity Support vector regression |
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