Beschreibung:
<jats:title>Abstract</jats:title><jats:p>Identifying the minimal number of parameters needed to describe a dataset is a challenging problem known in the literature as <jats:italic>intrinsic dimension estimation</jats:italic>. All the existing intrinsic dimension estimators are not reliable whenever the dataset is locally undersampled, and this is at the core of the so called <jats:italic>curse of dimensionality</jats:italic>. Here we introduce a new intrinsic dimension estimator that leverages on simple properties of the tangent space of a manifold and extends the usual correlation integral estimator to alleviate the extreme undersampling problem. Based on this insight, we explore a multiscale generalization of the algorithm that is capable of (i) identifying multiple dimensionalities in a dataset, and (ii) providing accurate estimates of the intrinsic dimension of extremely curved manifolds. We test the method on manifolds generated from global transformations of high-contrast images, relevant for invariant object recognition and considered a challenge for state-of-the-art intrinsic dimension estimators.</jats:p>