Second order optimality on orthogonal Stiefel manifolds

Orthogonal Nonnegative Matrix Factorization: Multiplicative Updates on Stiefel Manifolds

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonn...

Rolling Stiefel manifolds

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

Notes on Optimization on Stiefel Manifolds

Homogeneous Einstein metrics on Stiefel manifolds

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.

Filtering from Observations on Stiefel Manifolds

This paper considers the problem of optimal filtering for partially observed signals taking values on the rotation group. More precisely, one or more components are considered not to be available in the measurement of the attitude of a 3D rigid body. In such cases, the observed signal takes its values on a Stiefel manifold. It is demonstrated how to filter the observed signal through the anti-d...