Bayesian Topological Learning for Brain State Classification

TL;DR

This paper introduces a Bayesian topological approach using persistent homology to classify noisy, nonlinear, and nonstationary EEG signals, improving robustness and incorporating prior knowledge for brain state analysis.

Contribution

It presents a novel combination of topological data analysis and Bayesian inference to enhance EEG classification under challenging data conditions.

Findings

Outperforms existing EEG classification methods.

Effectively incorporates prior knowledge into analysis.

Demonstrates robustness to noise and nonstationarity.

Abstract

Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in human-machine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and nonstationary nature. Current methodologies for analyzing these signals often fall short because they have several regularity assumptions baked in. This work provides an effective, flexible and noise-resilient scheme to analyze EEG by extracting pertinent information while abiding by the 3N (noisy, nonlinear and nonstationary) nature of data. We implement a topological tool, namely persistent homology, that tracks the evolution of topological features over time intervals and incorporates individual's expectations as prior knowledge by means of a Bayesian framework to compute posterior distributions. Relying on these posterior distributions, we apply Bayes factor classification to noisy EEG measurements. The performance of this Bayesian classification scheme is then compared with other existing methods for EEG signals.