Principal component analysis as tool for data reduction with an application

Abstract

The recent trends in collecting huge datasets have posed a great challenge that is brought by the high dimensionality and aggravated by the presence of irrelevant dimensions. Machine learning models for regression is recognized as a convenient way of improving the estimation for empirical models. Popular machine learning models is support vector regression (SVR). However, the usage of principal component analysis (PCA) as a variable reduction method along with SVR is suggested. The principal component analysis helps in building a predictive model that is simple as it contains the smallest number of variables and efficient. In this paper, we investigate the competence of SVR with PCA to explore its performance for a more accurate estimation. Simulation study and Renal Failure (RF) data of SVR optimized by four different kernel functions; linear, polynomial, radial basis, and sigmoid functions using R software, version (R x64 3.2.5) to compare the behavior of ε SVR and v-SVR models for different sample sizes ranges from small, moderate to large such as; 50, 100, and 150. The performance criteria are root mean squared error (RMSE) and coefficient of determination R2 showed the superiority of ε-SVR over v- SVR. Furthermore, the implementation of SVR after employing PCA improves the results. Also, the simulation results showed that the best performing kernel function is the linear kernel. For real data the results showed that the best kernels are linear and radial basis function. It is also clear that, with ε-SVR and v-SVR, the RMSE values for almost kernel functions decreased with increasing sample size. Therefore, the performance of ε-SVR improved after applying PCA. In addition sample size n=50 gave good results for linear and radial kernel