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Sunday, July 19 • 9:00pm - 10:00pm
P126: Topological Byesian Signal Processing with Application to EEG

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Christopher Oballe, Alan Czerne, David Boothe, Scott Kerick, Piotr Franaszczuk, Vasileios Maroulas

Electroencephalography is a neuroimaging technique that works by monitoring electrical activity in the brain. Electrodes are placed on the scalp and local changes in voltage are measured over time to produce a collection of time series known as electroencephalograms (EEGs). Traditional signal processing metrics, such as power spectral densities (PSDs), are generally used to analyze EEG since frequency content of EEG is associated with different brain states. Conventionally, PSD estimates are obtained via discrete Fourier transforms. While this method effectively detects low-frequency components because of their high powers, high-frequency activity may go unnoticed because of its relatively weaker power. We employ a topological Bayesian approach that successfully captures even these low-power, high-frequency components of EEG.

Topological data analysis encompasses a broad set of techniques that investigate the shape of data. One of the predominant tools in topological data analysis is persistent homology, which creates topological descriptors called persistence diagrams from datasets. In particular, persistent homology offers a novel technique for time series analysis. To motivate our use of persistent homology to study frequency content of signals, we establish explicit links between features of persistence diagrams, like cardinality and spatial distributions of points, to those of the Fourier series of deterministic signals, specifically the location of peaks and their relative powers. The topological Bayesian approach allows for quantification of these cardinality and spatial distributions by modelling persistence diagrams as marked Poisson point processes.

We test our Bayesian topological method to classify synthetic EEG. We employ three common classifiers: linear regression and support vector machines with linear and radial kernels, respectively. We simulate synthetic EEG with an autoregressive (AR) model, which works by recasting a standard AR model as linearly filtered white noise, enabling straightforward computation of PSDs. The AR model allows us to control the location and width of peaks in PSDs. With this model in hand, we create five classes of signals with peaks in their PSDs at zero to simulate the approximate 1/f behavior of EEG PSDs, four of which also have oscillatory components at 6 Hz (theta), 10 Hz (alpha), 14 Hz (low beta), and 21 Hz (high beta); the fifth class (null) lacks any such component. We repeat this process for two different widths of peaks, narrow (4 Hz) and wide (32 Hz). With data in hand, we extract features using periodograms, persistence diagrams, and our Bayesian topological method, then independently use these features in classification for the wide and narrow width cases. Preliminarily, while both the Bayesian topological method and periodogram features obtain near perfect for the narrow peak case, the Bayesian topological method outperforms the periodogram features over all tested classifiers in the wide peak case.


Sunday July 19, 2020 9:00pm - 10:00pm CEST
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