Intrinsic dimension estimation: Advances and open problems

Dimensionality reduction methods are preprocessing techniques used for coping with high dimensionality. They have the aim of projecting the original data set of dimensionality N, without information loss, onto a lower M-dimensional submanifold. Since the value of M is unknown, techniques that allow knowing in advance the value of M, called intrinsic dimension (ID), are quite useful. The aim of the paper is to review state-of-the-art of the methods of ID estimation, underlining the recent advances and the open problems. (C) 2015 Elsevier Inc. All rights reserved.