关键词: LGA, 全最小一乘, 稳健性, 聚类分析

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.

Key words: Linear Grouping Algorithm (LGA), total least absolute deviations, robustness, cluster analysis