Directional median analysis

The Directional Median Analysis is a new proposal of robust data exploration. It can be treated as a multivariate extension of the idea similar to Theil-Sen estimator, where one finds a direction which minimizes the sum of angles to all observations. Theoretical analysis of this problem reveals that this analysis can be perceived as a special case of Spherical PCA and further robustifies the Spherical PCA analysis. Data decomposition can be done sequentially and each direction can be obtained by iterative reweighting. The idea is compared with classical PCA and Spherical PCA. A comparison on two artificial datasets shows that this method works more robust than Spherical PCA and could be promising alternative (or additive) to known robust data analysis methods.