Nonlinear Robust Regression Using Kernel Principal Component Analysis and R-Estimators
In recent years, many algorithms based on kernel principal component analysis (KPCA) have been proposed including kernel principal component regression (KPCR). KPCR can be viewed as a non-linearization of principal component regression (PCR) which uses the ordinary least squares (OLS) for estimating its regression coefficients. We use PCR to dispose the negative effects of multicollinearity in regression models. However, it is well known that the main disadvantage of OLS is its sensitiveness to the presence of outliers. Therefore, KPCR can be inappropriate to be used for data set containing outliers. In this paper, we propose a novel nonlinear robust technique using hybridization of KPCA and R-estimators. The proposed technique is compared to KPCR and gives better results than KPCR.
Keywords: Kernel principal component analysis, kernel principal component regression, robustness, nonlinear robust regression, R-estimators.
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ABOUT THE AUTHORS
Antoni Wibowo
Antoni Wibowo is currently working as a senior lecturer in the faculty of computer science and information systems, UTM. He received B.Sc in Math Engineering from University of Sebelas Maret (UNS) Indonesia and M.Sc in Computer Science from University of Indonesia. He also received M. Eng and Dr. Eng in System and Information Engineering from University of Tsukuba Japan. His interests are in the field of computational intelligence , operations research and data analysis.
Mohammad Ishak Desa
Mohamad Ishak Desa is　a professor in the faculty of computer science and information systems, UTM. He received his B.Sc. in Mathematics from UKM in Malaysia, a postgraduate diploma in system analysis from Aston University, UK. He also received a M.A. in Mathematics from University of Illinois at Springfield, USA and then, a PhD in operations research from　Salford University, UK. He is currently the Head of the Operations and Business Intelligences Research Group in UTM. His interests are operations research, optimization, logistic and supply chain, and computational intelligence.
Antoni Wibowo
Antoni Wibowo is currently working as a senior lecturer in the faculty of computer science and information systems, UTM. He received B.Sc in Math Engineering from University of Sebelas Maret (UNS) Indonesia and M.Sc in Computer Science from University of Indonesia. He also received M. Eng and Dr. Eng in System and Information Engineering from University of Tsukuba Japan. His interests are in the field of computational intelligence , operations research and data analysis.
Mohammad Ishak Desa
Mohamad Ishak Desa is　a professor in the faculty of computer science and information systems, UTM. He received his B.Sc. in Mathematics from UKM in Malaysia, a postgraduate diploma in system analysis from Aston University, UK. He also received a M.A. in Mathematics from University of Illinois at Springfield, USA and then, a PhD in operations research from　Salford University, UK. He is currently the Head of the Operations and Business Intelligences Research Group in UTM. His interests are operations research, optimization, logistic and supply chain, and computational intelligence.
