Geometric Machine Learning on EEG Signals

2025-02-07

AI Summary

To address the challenges of decoding low-dimensional geometric structures from high-dimensional EEG signals and poor model interpretability, this paper proposes a two-stage geometric machine learning framework. In the first stage, a channel-wise attention mechanism suppresses noise in individual EEG channels. In the second stage, Fourier transform, Laplacian eigenmaps, Ollivier curvature-guided discrete Ricci flow, and graph convolutional networks are jointly integrated to explicitly model the manifold structure underlying multi-channel EEG. Notably, this work introduces discrete Ricci flow to EEG analysis for the first time, synergistically coupling differential-geometric priors with deep learning to achieve interpretable and regularizable geometric modeling of neural signals. Evaluated on a semi-synthetic denoising task, the method achieves a correlation coefficient of 0.952 at SNR = 2 dB; for imagined-digit classification, it attains 97.0% accuracy—substantially outperforming state-of-the-art approaches.

Technology Category

• Machine Learning: Learning with Manifolds
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

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.

Problem

• Decoding high-dimensional EEG signals
• Geometric structure in brainwave data
• BCI-related neural classification tasks

Innovation

• Attention-based EEG noise filtration
• Laplacian eigenmap for dimensionality reduction
• Graph convolutional network for EEG classification