Geometric Machine Learning on EEG Signals

TL;DR

This work addresses decoding high-dimensional EEG signals by revealing a low-dimensional geometric structure that can improve BCI classification. It introduces a denoising stage (AT-AT) to clean single-channel EEGs and a downstream manifold-learning pipeline that fuses FFT features with Laplacian eigenmaps, Ricci-flow refined graphs via Ollivier-Ricci curvature, and graph convolutional networks to produce geometry-aware embeddings for simple downstream classifiers. Results on semi-synthetic denoising and open-set imagined digit tasks show competitive performance, with a mean CC around 0.95 at moderate noise and digit-vs-non-digit accuracy near 0.97, though validation is preliminary and generalization remains a priority. If validated broadly, this geometric ML approach could enable more robust, scalable EEG interpretation and inspire future work on the geometric structure of brain activity, while also necessitating careful handling of privacy and ethical considerations.

Abstract

Brain-computer interfaces (BCIs) offer transformative potential, but decoding neural signals presents significant challenges. The core premise of this paper is built around demonstrating methods to elucidate the underlying low-dimensional geometric structure present in high-dimensional brainwave data in order to assist in downstream BCI-related neural classification tasks. We demonstrate two pipelines related to electroencephalography (EEG) signal processing: (1) a preliminary pipeline removing noise from individual EEG channels, and (2) a downstream manifold learning pipeline uncovering geometric structure across networks of EEG channels. We conduct preliminary validation using two EEG datasets and situate our demonstration in the context of the BCI-relevant imagined digit decoding problem. Our preliminary pipeline uses an attention-based EEG filtration network to extract clean signal from individual EEG channels. Our primary pipeline uses a fast Fourier transform, a Laplacian eigenmap, a discrete analog of Ricci flow via Ollivier's notion of Ricci curvature, and a graph convolutional network to perform dimensionality reduction on high-dimensional multi-channel EEG data in order to enable regularizable downstream classification. Our system achieves competitive performance with existing signal processing and classification benchmarks; we demonstrate a mean test correlation coefficient of >0.95 at 2 dB on semi-synthetic neural denoising and a downstream EEG-based classification accuracy of 0.97 on distinguishing digit- versus non-digit- thoughts. Results are preliminary and our geometric machine learning pipeline should be validated by more extensive follow-up studies; generalizing these results to larger inter-subject sample sizes, different hardware systems, and broader use cases will be crucial.

Figures (7)

• Figure 1: AT-AT processing facilitates latent space separability of neural signal classes. Pre-AT-AT t-SNE depicted left; post-AT-AT depicted right.
• Figure 2: The six manifold learning pipeline stages. (1) AT-AT filtration; (2) FFT upscaling and Laplacian eigenmap reduction; (3) graph initialization; (4) Ricci flow evolution; (5) edge cutting; (6) final representation for GCN reduction.
• Figure 3: Class embeddings produced by the GCN after the manifold learning pipeline.
• Figure 4: Summary of Ollivier-Ricci curvature pipeline metrics as described in sec:Methods2SectionSections.
• Figure 5: Estimated true performance on the open-set imagined digit recognition problem with our geometric machine learning pipeline when combined with the top claimed inter-digit classification performance in literature mahapatra.