An evaluation of intrinsic dimensionality estimators

The intrinsic dimensionality of a data set may be useful for understanding the properties of classifiers applied to it and thereby for the selection of an optimal classifier. In this paper the authors compare the algorithms for two estimators of the intrinsic dimensionality of a given data set and extend their capabilities. One algorithm is based on the local eigenvalues of the covariance matrix in several small regions in the feature space. The other estimates the intrinsic dimensionality from the distribution of the distances from an arbitrary data vector to a selection of its neighbors. The characteristics of the two estimators are investigated and the results are compared. It is found that both can be applied successfully, but that they might fail in certain cases. The estimators are compared and illustrated using data generated from chromosome banding profiles