This book constitutes the refereed proceedings of the Second International Conference on Geometric Science of Information, GSI 2015, held in Palaiseau, France, in October 2015.

The 80 full papers presented were carefully reviewed and selected from 110 submissions and are organized into the following thematic sessions:

Dimension reduction on Riemannian manifolds; optimal transport; optimal transport and applications in imagery/statistics; shape space and diffeomorphic mappings; random geometry/homology; Hessian information geometry; topological forms and Information;...