Classification of biological signals on the symmetric positive definite manifold

Biological signal classification plays an important role in health-related real-time applications. It has been shown that using a covariance matrix representation of biological signals and exploiting the Riemannian geometry of the space of symmetric positive definite (SPD) matrices, to which covariance matrices belong, enables to ease signal discrimination. Unfortunately, classifying points on high-dimensional SPD manifolds is computationally expensive, so not well-suited for real-time applications. In this thesis, we propose to combine the covariance matrix representation with a structure-preserving dimensionality reduction algorithm. Namely, we define a mapping from a high-dimensional SPD manifold to a lower-dimensional SPD manifold, that preserves the intrinsic structure of the data. We combine this dimensionality reduction algorithm with two classification algorithms on Riemannian manifolds (i.e. minimum distance to Riemannian mean (MDRM) and k-nearest neighbors (KNN)) and test these approaches in two different setups: electroencephalography (EEG) and surface electromyography (sEMG). We show that we can reduce the computational time while gaining classification performance.