On the Pulling Linear Regression and Its Applications in Digital Mammograms

Abstract

Regression analysis is a statistical approach used to investigate the correlations between variables, especially linear regression, that is a simple but effective approach for analyzing the relationship between a dependent variable and one independent variable. Since it has limitations based on the assumption that the mean of the noise should be zero, there are still some areas where it may be improved. In this article, we introduce a novel data fitting algorithm called the pulling linear regression, which is separated into two types: the line-pulling linear regression and the band-pulling linear regression. The method is developed from linear regression, which can create the regression line from the function that uses noise with various distributions. The result demonstrates that the sequence of sum square errors of the pulling linear regression is convergent. Moreover, we have a numerical example to show that the performance of the proposed algorithm is better than that of linear regression when the mean of the noise is not zero. And the last, we have an application to smooth the boundary of the pectoral muscle in digital mammograms. We found that the regression line of the proposed algorithm can do better than the linear regression when we would like to remove only the muscle part.