Persistent homology of toroidal sliding window embeddings

Jose A. Perea

ICASSP 2016accepted0 citations

Persistent homology of toroidal sliding window embeddings

Abstract

In this paper we study the persistent homology of sliding window embeddings of quasi-periodic signals. That is, functions which are sums of harmonics with different periods, and in particular, those having incommensurate frequencies. The resulting sliding window point-clouds, in this case, are (dense in) high-dimensional tori. We prove theorems which guide the choice of window size and embedding dimension, and describe the associated persistent homology.

BibTeX

@inproceedings{icassp2016_persistenthomolo,
  title = {Persistent homology of toroidal sliding window embeddings},
  author = {Jose A. Perea},
  booktitle = {ICASSP 2016},
  year = {2016}
}