An empirical evaluation of intrinsic dimension estimators

We study the practical behavior of different algorithms and methods that aim to estimate the intrinsic dimension (IDim) in metric spaces. Some of them were specifically developed to evaluate the complexity of searching in metric spaces, based on different theories related to the distribution of distances between objects on such spaces. Others were originally designed for vector spaces only, and have been extended to general metric spaces. To empirically evaluate the fitness of various IDim estimations with the actual difficulty of searching in metric spaces, we compare two representatives of each of the broadest families of metric indices: those based on pivots and those based on compact partitions. Our conclusions are that the estimators Distance Exponent and Correlation fit best their purpose.