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arXiv · 1902.03840

On the Rotational Invariant $L_1$-Norm PCA

Sebastian Neumayer·Max Nimmer·Simon Setzer·Gabriele Steidl
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Abstract

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.

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Sebastian Neumayer, Max Nimmer, Simon Setzer, Gabriele Steidl. 2019-02-11. On the Rotational Invariant $L_1$-Norm PCA. https://arxiv.org/abs/1902.03840

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