Minimum neighbor distance estimators of intrinsic dimension

Abstract

Most of the machine learning techniques suffer the "curse of dimensionality" effect when applied to high dimensional data. To face this limitation, a common preprocessing step consists in employing a dimensionality reduction technique. In literature, a great deal of research work has been devoted to the development of algorithms performing this task. Often, these techniques require as parameter the number of dimensions to be retained; to this aim, they need to estimate the "intrinsic dimensionality" of the given dataset, which refers to the minimum number of degrees of freedom needed to capture all the information carried by the data. Although many estimation techniques have been proposed, most of them fail in case of noisy data or when the intrinsic dimensionality is too high. In this paper we present a family of estimators based on the probability density function of the normalized nearest neighbor distance. We evaluate the proposed techniques on both synthetic and real datasets comparing their performances with those obtained by state of the art algorithms; the achieved results prove that the proposed methods are promising. © 2011 Springer-Verlag.