Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

This paper has three main objectives.

1. First, to provide a simple overview of the challenges of selecting good embedding parameters.
2. Second, to collate and compare the various popular methods across the dynamics-topology spectrum that have been proposed to tackle the problem of embedding parameter selection. We will focus on the particular case of optimizing time delay embedding.
3. Finally, to present a different approach based on the growing field of persistent homology—the significance score—that attempts to incorporate both dynamical and topological arguments into selection of embedding parameters.