Riemannian adaptive stochastic gradient algorithms on matrix manifolds

Understand

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately.

• Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging.
• This is because of the intrinsic non-linear structure of the underlying manifold and the absence of a canonical coordinate system.
• In machine learning applications, however, most manifolds of interest are represented as matrices with notions of row and column subspaces.