Title: Nested Homogeneous Spaces: Construction, Learning and Applications
Abstract: Homogeneous space of a Lie Group G, is a manifold M on which the group G acts transitively.
Intuitively, every point in a homogeneous space looks locally alike in the sense of an isometry, diffeomorphism
or a homeomorphism. Such spaces are abundant in practice e.g., the n-sphere, Grassmanian,
hyperbolic space, manifold of symmetric positive definite matrices etc. In statistics and machine learning,
principal component analysis is the de facto choice for dimensionality reduction and produces nested
linear subspaces. In this talk, I will present a recipe for generalizing this concept of producing nested
subspaces to homogeneous spaces in general, and show how this general recipe can be integrated into a
learning framework. Specific examples of dimensionality reduction and pattern classification using the
nested homogeneous space model will be presented for the Grassmanian and the hyperbolic space. In the
latter case, the nested hyperbolic space model will be used to develop a nested hyperbolic graph neural
network. Experimental results on a variety of synthetic and real data sets depicting the performance of
the models in comparison to the state-of-the-art will be interspersed throughout the presentation.
Here is the zoom link is: https://wse.zoom.us/j/95448608570