Structure-Preserving Transformers for Sequences of SPD Matrices

TL;DR

This paper introduces a Transformer-based method that preserves the Riemannian geometry of SPD matrices for sequence classification, demonstrated on EEG covariance data for sleep staging with high accuracy.

Contribution

The paper proposes a novel structure-preserving Transformer architecture tailored for sequences of SPD matrices, maintaining their geometric properties during analysis.

Findings

Achieved high sleep staging accuracy on EEG covariance matrices.

Demonstrated effectiveness of geometry-preserving attention mechanisms.

Validated approach on a standard sleep dataset.

Abstract

In recent years, Transformer-based auto-attention mechanisms have been successfully applied to the analysis of a variety of context-reliant data types, from texts to images and beyond, including data from non-Euclidean geometries. In this paper, we present such a mechanism, designed to classify sequences of Symmetric Positive Definite matrices while preserving their Riemannian geometry throughout the analysis. We apply our method to automatic sleep staging on timeseries of EEG-derived covariance matrices from a standard dataset, obtaining high levels of stage-wise performance.