With Stéphane Mussard and Téa Ouraga, we recently uploaded on arxiv a paper Principal Component Analysis: A Generalized Gini Approach,

A principal component analysis based on the generalized Gini correlation index is provided. It is proven that the reduction dimensionality based on the generalized Gini correlation index, that relies on city-block distances, is robust to outliers.

Some codes are also available on a dedicated github repo.