Intrinsic Dimensionality Estimation of Submanifolds in R
We present a new method to estimate the intrinsic dimensionality of a submanifold M in R from random samples. The method is based on the convergence rates of a certain U -statistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover the proposed method is easy to implement, can handle large data sets and performs very well even for small sample sizes. We compare the proposed method to two standard estimators on several artificial as well as real data sets.