Outlier elimination using granular box regression

Abstract

A regression method desires to fit the curve on a data set irrespective of outliers. This paper modifies the granular box regression approaches to deal with data sets with outliers. Each approach incorporates a three-stage procedure includes granular box configuration, outlier elimination, and linear regression analysis. The first stage investigates two objective functions each applies different penalty schemes on boxes or instances. The second stage investigates two methods of outlier elimination to, then, perform the linear regression in the third stage. The performance of the proposed granular box regressions are investigated in terms of: volume of boxes, insensitivity of boxes to outliers, elapsed time for box configuration, and error of regression. The proposed approach offers a better linear model, with smaller error, on the given data sets containing varieties of outlier rates. The investigation shows the superiority of applying penalty scheme on instances.