LTSD: a highly efficient symmetry-based robust estimator

Although the least median of squares (LMedS) method and the least trimmed squares (LTS) method are said to have a high breakdown point (50%), they can break down at unexpectedly lower percentages of outliers when those outliers are clustered. In this paper, we investigate the breakdown of LMedS and the LTS when a large percentage of clustered outliers exist in the data. We introduce the concept of symmetry distance (SD) and propose an improved method, called the least trimmed symmetry distance (LTSD). The experimental results show the LTSD gives better results than the LMedS method and the LTS method particularly when there is a large percentage of clustered outliers and/or a large standard variance in the inlier population.