DANCo: An intrinsic dimensionality estimator exploiting angle and norm concentration

In the past decade the development of automatic intrinsic dimensionality estimators has gained considerable attention due to its relevance in several application fields. However, most of the proposed solutions prove to be not robust on noisy datasets, and provide unreliable results when the intrinsic dimensionality of the input dataset is high and the manifold where the points are assumed to lie is nonlinearly embedded in a higher dimensional space. In this paper we propose a novel intrinsic dimensionality estimator (DANCo) and its faster variant (FastDANCo), which exploit the information conveyed both by the normalized nearest neighbor distances and by the angles computed on couples of neighboring points. The effectiveness and robustness of the proposed algorithms are assessed by experiments on synthetic and real datasets, by the comparative evaluation with state-of-the-art methodologies, and by significance tests.