  Principal component analysis (PCA) is a powerful tool for dimensionality
reduction. Unfortunately, it is sensitive to outliers, so that various robust
PCA variants were proposed in the literature. Among them the so-called
rotational invariant $L_1$-norm PCA is rather popular. In this paper, we
reinterpret this robust method as conditional gradient algorithm and show
moreover that it coincides with a gradient descent algorithm on Grassmannian
manifolds. Based on this point of view, we prove for the first time convergence
of the whole series of iterates to a critical point using the
Kurdyka-{\L}ojasiewicz property of the energy functional.
