Geometric feature performance under downsampling for EEG classification tasks
This work addresses benchmarking gaps for EEG classification with geometric features, though it is incremental as it applies known topological methods to a specific dataset.
The study investigated geometric feature engineering pipelines for classifying eyes-open vs. eyes-closed EEG data using CNNs, finding that topological invariants like Betti-numbers and graph spectra performed comparably to raw time-series but showed varying robustness to downsampling.
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 $ε$-series of Betti-numbers and $ε$-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.