Data dimensionality estimation: Achievements and challanges

Dimensionality Reduction methods are effective preprocessing techniques that clustering algorithms can use for coping with high dimensionality. Dimensionality Reduction methods have the aim of projecting the original data set of dimensionality d, minimizing 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 make the state-of-art of the methods of intrinsic dimensionality estimation, underlining the achievements and the challanges