Abstract
•We propose that the recently defined persistent homology (PHi) dimensions are a practical tool for dimension estimation.•We implement an algorithm to compute the PHi dimensions and apply it to a variety of examples, including self-similar fractals, chaotic attractors, and earthquake hypocenters.•The accuracy and speed of the PH0 dimension estimation algorithm is comparable to that of the correlation dimension, and better than the box-counting dimension.
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance to classical methods to compute the correlation and box-counting dimensions in examples of self-similar fractals, chaotic attractors, and an empirical dataset. The performance of the 0-dimensional persistent homology dimension is comparable to that of the correlation dimension, and better than box-counting.