Persistent Homology of Time-Delay Embeddings

Thursday, October 10, 2013 - 9:00am - 9:50am
Keller 3-180
Jose Perea (Duke University)
We present in this talk a theoretical framework for studying the
persistent homology of point clouds from time-delay (or sliding window)
embeddings. We will show that maximum 1-d persistence yields a suitable
measure of periodicity at the signal level, and present theorems which
relate the resulting diagrams to the choices of window size, embedding
dimension and field of coefficients. If time permits, we will
demonstrate how this methodology can be applied to the study of
periodicity on time series from gene expression data.
MSC Code: