Investigation of the maximum likelihood estimator of intrinsic dimensionality

Abstract

Real-life data are often hardly understandable because of their high-dimen- sionality. Therefore, the knowledge about the intrinsic dimensionality of a data set is very useful. Several methods for estimating the intrinsic dimensionality are proposed in the literature. In this paper, the maximum likelihood estimator (MLE) for the intrinsic dimensionality is analyzed. We propose the way how to improve the estimates of the intrinsic dimensionality. Directions for further investigations are highlighted.