SPDNet-AE: a Compact SPD Representation through Riemannian Autoencoding

When building dimension reduction methods tailored for Symmetric Positive Definite (SPD) matrices, it is crucial to account for their Riemannian geometry. In this work, we propose an SPDNet-based autoencoder, that we call SPDNet-AE, that learns low-dimensional SPD representations of high-dimensional SPD matrices while preserving the geometry throughout the network. The SPDNet-AE is built using the BiMap layer of the SPDNet, but we allow it to have multiple channels. We show that our SPDNet-AE is able to learn a useful low-dimensional representation of the data for classification (without any class information). Moreover, we show that with a comparable number of parameters, a classical Euclidean autoencoder is not able to learn and maintain the SPD constraint on the input matrices.