Towards persistence-based reconstruction in euclidean spaces
Frédéric Chazal, Steve Oudot · 2008
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recent advances in higher dimensions have led to new methods to reconstruct large classes of compact subsets of Rd. However, the complexities of these methods scale up exponentially with d, making them impractical in medium or high dimensions, even on data sets of low intrinsic dimensionality.