Application of weighted low rank approximations: outlier detection in a data matrix

Six criteria for identifying outliers from weighted approximations were considered, including simple residuals, squared residuals with differential weights, Jackknife and their corresponding iterative versions, and they were compared with the gold standard one based on limits from a bias-adjusted boxplot. All methods are applicable to any numerical data set written in matrix form, e.g. experiments with genotype-by-environment interaction. It was found that in the presence of random outliers in a matrix with numerical entries, the identification of outliers using weighted approximations is more effective than detection based on limits from a bias-adjusted boxplot.