turkmath.org

Many datasets consist of complex items that can be reasonably surmised to lie on a manifold of much lower dimension than the number of parameters or coordinates with which the individual items are acquired. Manifold diffusion is an established method, used successfully to parametrize such datasets much more succinctly. The talk describes an enhancement of this method: when each individual item is itself a complex object, as is the case in many applications, one can model the collection as a fiber bundle, and build a fiber bundle diffusion operator from which one can gradually learn properties of the underlying base manifold. This will be illustrated with applications to morphological evolutionary studies in biology.