We consider applications involving a large set of instances projecting points to polytopes. develop an intuition guided by theoretical and empirical analysis show that when these follow certain structures, majority the projections lie on vertices To do efficiently we derive vertex-oriented incremental algorithm project point onto any arbitrary polytope, as well give specific algorithms cater si...

We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input unknown linear transformations of some latent vectors drawn from polytope. sense, the article considers semi-structured model, in which matrix is modeled product full column rank and containing samples polytope its vectors. The choice reflects presumed features compone...