On intrinsic dimension of point clouds by a persistent homology approach: computational tips

We present new results on estimating the intrinsic dimension (ID) of point clouds using persistent homology. In particular, we compare topological ID estimators with different approaches, comprehensively assessing their strengths and weaknesses. We show that a combination of the so-called i-dimensional persistent homology fractal dimension estimator and the persistent homology dimension, which we termed i-dimensional α persistent homology fractal dimension, is a suitable choice for obtaining an effective estimation of the ID in many benchmark datasets.