An Empirical Evaluation of Intrinsic Dimension Estimators

In this work, we study the behavior of different algorithms that attempt to estimate the intrinsic dimension (ID) in metric spaces. Some of these algorithms were developed specifically for evaluating the complexity of the search on metric spaces, based on different theories related to the distribution of distances between objects on such spaces. Others were designed originally only for vector spaces and they have been adapted so that they can be applied to metric spaces. To determine the goodness of the ID estimation obtained with each algorithm —or at least determine which one fits the best to the actual difficulty of the search process on the tested metric spaces— we make comparisons using two indices, one based on pivots and the other on compact partitions. This allows us to verify if the considered ID estimators reflect the actual hardness of searching over the considered spaces.