Mainstream statistical methodology is generally applicable to data observed in Euclidean
space. There are, however, numerous contexts of considerable scientific interest in which …

Deep Learning (DL) has achieved remarkable success in tackling complex Artificial
Intelligence tasks. The standard training of neural networks employs backpropagation to …

In video based face recognition, great success has been made by representing videos as
linear subspaces, which typically lie in a special type of non-Euclidean space known as …

Learning representations on Grassmann manifolds is popular in quite a few visual
recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper …

Recent work on mid-level visual representations aims to capture information at the level of
complexity higher than typical visual words", but lower than full-blown semantic objects …

We consider kernel methods on general geodesic metric spaces and provide both negative
and positive results. First we show that the common Gaussian kernel can only be …

Recent advances in computer vision and machine learning suggest that a wide range of
problems can be addressed more appropriately by considering non-Euclidean geometry. In …

The attention paid to matrix manifolds has grown considerably in the computer vision
community in recent years. There are a wide range of important applications including face …

Sparsity-based representations have recently led to notable results in various visual
recognition tasks. In a separate line of research, Riemannian manifolds have been shown …

This book collects important advances in methodology and data analysis for directional
statistics. It is the companion book of the more theoretical treatment presented in Modern …