  We experimentally investigate a collection of feature engineering pipelines
for use with a CNN for classifying eyes-open or eyes-closed from
electroencephalogram (EEG) time-series from the Bonn dataset. Using the Takens'
embedding--a geometric representation of time-series--we construct simplicial
complexes from EEG data. We then compare $\epsilon$-series of Betti-numbers and
$\epsilon$-series of graph spectra (a novel construction)--two topological
invariants of the latent geometry from these complexes--to raw time series of
the EEG to fill in a gap in the literature for benchmarking. These methods,
inspired by Topological Data Analysis, are used for feature engineering to
capture local geometry of the time-series. Additionally, we test these feature
pipelines' robustness to downsampling and data reduction. This paper seeks to
establish clearer expectations for both time-series classification via
geometric features, and how CNNs for time-series respond to data of degraded
resolution.
