An Algorithm of Detecting Outliers in SVR

Abstract

This paper defines an outlier and a measure that an outlier does not fit the theoretical model in the regression problems, studies the relationship between the theoretical model and the regression model in the regression problems, proposes and verifies an approximate theorem in which one-by-one deletes outlier and constructs SVR to approximate its theoretical model, draws an algorithm of detecting outliers in the SVR problems based on the approximate theorem, and analyzes the convergence and effectiveness of the algorithm in the theory. Next, it combines the step-by-step search algorithm were proposed by authors and the former detecting outlier algorithm to improve it, and brings forward an algorithm detecting outliers in SVR based on large-scale samples. Then, its analysis in theory shows the improved algorithm is convergent and effective too. Finally, its simulation results show that the detecting outlier algorithms are effective and robust, using samples produced by two test functions and in UCI dataset.