We present several methods for multi-manifold data modeling,
i.e., modeling data by mixtures of possibly intersection manifolds.
We focus on algorithms for the special case of hybrid linear modeling, that is,
where the underlying manifolds are affine or linear subspaces. We emphasize
various theoretical results supporting the performance of
some of these algorithms, in particular their robustness to noise
and outliers. We demonstrate how such theoretical insights guide us in
practical choices. We also present various applications of such algorithms.
This is part of various joint works with E. Arias-Castro, S. Atev, G. Chen,
A. Szlam, Y. Wang, T. Whitehouse and T. Zhang
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