  It is well known that Principal Component Analysis (PCA) is strongly affected
by outliers and a lot of effort has been put into robustification of PCA. In
this paper we present a new algorithm for robust PCA minimizing the trimmed
reconstruction error. By directly minimizing over the Stiefel manifold, we
avoid deflation as often used by projection pursuit methods. In distinction to
other methods for robust PCA, our method has no free parameter and is
computationally very efficient. We illustrate the performance on various
datasets including an application to background modeling and subtraction. Our
method performs better or similar to current state-of-the-art methods while
being faster.
