New linear grouping algorithm based on total least absolute deviation criteria

Abstract

To overcome the drawback that the traditional Linear Grouping Algorithm(LGA),when extracting linear structures,is sensitive to outliers in datasets,a new finite step according to existence of optimal linear grouping in data set and a new algorithm based on k-means clustering,total least absolute deviation and resampling were proposed,which detected several different linear relations at once to minimize the total orthogonal distances from n given points to its nearest hyperplanes.Finally,by comparison with linear grouping algorithm and robust linear grouping algorithm based on impartial trimmed k-means,the proposed algorithms are more robust and can detect all strong linear structures in datasets including a lot of outliers.