A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data. In this work, we study the setting where the data (or measurements) are ordered, longitudinal or temporal in nature and live on a Riemannian manifold -- this setting is common in a variety of problems in statistical machine learning, vision and medical imaging. We show how recurrent statistical recurrent network models can be defined in such spaces.