About One Robust Variant of Principal Component Analysis

A new robust version of the classical formulation of the problem of finding principal components, dating back to Pearson, is considered. It is based on the use of differentiable estimates of the mean value, insensitive or slightly sensitive to outliers, to construct a robust version of the objective functional in the corresponding optimization problem. This approach, in principle, makes it possible to overcome the impact of outliers. The capabilities of the proposed approach to overcome the impact of outliers are clearly demonstrated using real data.