🍩 Database of Original & Non-Theoretical Uses of Topology

1. Use of Topological Data Analysis in Motor Intention Based Brain-Computer Interfaces (2018)

   Fatih Altindis, Bulent Yilmaz, Sergey Borisenok, Kutay Icoz

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   • Brain-computer interface
   • Motion
   • Neurology
   • EEG
   • Electric signals
   • Electroencephalogram
   • Betti numbers
   • Persistent homology

2. Geometric Feature Performance Under Downsampling for EEG Classification Tasks (2021)

   Bryan Bischof, Eric Bunch

   Abstract

   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.

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   • Classification neural networks
   • Machine learning
   • Neurology
   • EEG
   • Electric signals
   • Electroencephalogram
   • Time series
   • ε-series of Betti-numbers
   • ε-series of graph spectra