Abstract
We study the persistent topological features of a reconstructed time series via
a simplicial complex called a witness complex. Using deterministic and nondeterministic
time series, we examine topological features that persist over
a range of parameter values. Phase-space reconstruction is used to initially
analyze the time series, converting it to a point cloud data. Most time series
have hidden topological properties which can be unfolded by doing phase
space reconstruction. Here we only use a small subset of the reconstructed
time series (called a landmark set). We compute the topological features of
the witness complex associated to the landmark set and monitor persistent
Betti numbers. We show that with correct reconstruction parameters and
range of landmarks, that the reconstructed time series gives the accurate
homology of the time series.
M.Sc. (Applied Mathematics)