Density support and intrinsic dimension estimation based on a hierarchical delaunay-type simplicial complex
Résumé
Let $X_1,...,X_N$, $X_i\in \mathbb{R}^D$ be an uniform drawn on a compact $d-$dimensional manifold $S$ with $d\leq D$. Here is suggested a new way to estimate both $S$ and $d$. The method is based on the computation of a set of simplicial complexes (one for each dimension $d\leq D$) and on an inductive criterion to select the ''good'' one. Each computed complex is a subcomplex of Delaunay's complex computed using $k-$nearest neighbors restriction and local $PCA$. A proposition for the $k$ value is given in the first part and the algorithm is detailed in the second part.
Domaines
Autres [stat.ML]
Origine : Fichiers produits par l'(les) auteur(s)