An Empirical Evaluation of Intrinsic Dimension Estimators
Gonzalo Navarro, Rodrigo Paredes, Nora Reyes, and Cristian Bustos
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
related to the distribution of distances between objects on such spaces.
originally designed for vector spaces only, and have been extended to general
metric spaces. To empirically evaluate the fitness of various IDim estimations
the actual difficulty of searching in metric spaces, we compare two
of each of the broadest families of metric indices: those based on pivots and
based on compact partitions. Our conclusions are that the estimators
Distance Exponent and Correlation fit best their purpose.