“Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, Vk(ℝN) and Gr(k,ℝN) respectively, and benefit from projection onto lower-dimensional Stiefel (respectively, Grassmannian) manifolds. In this work, we propose an algorithm called Principal Stiefel Coordinates (PSC) to reduce data dimensionality from Vk(ℝN) to Vk(ℝn) in an O(k)-equivariant manner (k≤n≪N).”

Find the paper and full list of authors at ArXiv.