Sampling From A Manifold

On images of continuous functions from a compact manifold to Euclidean space

Tangent Space Estimation for Smooth Embeddings of Riemannian Manifolds

Numerous dimensionality reduction problems in data analysis involve the recovery of lowdimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a point from locally available data samples. Local sampling conditions such as (i) the size of the neighborhood (sampling width) and (ii) the n...

Manifold Representations for State Estimation in Contact Manipulation

We investigate the problem of using contact sensors to estimate the configuration of an object during manipulation. Contact sensing is very discriminative by nature and, therefore, the set of object configurations that activate a sensor constitutes a lower-dimensional manifold in the configuration space of the object. This causes conventional state estimation methods, such as particle filters, ...

Orbit Theorems and Sampling

This paper proposes a notion of smooth action on a manifold, and establishes a general integrability result for certain associated distributions. As corollaries, various classical and new results on manifold structures of orbits are established, and the main theorem on preservation of transitivity under sampling is shown to be a simple consequence.

Manifold Sampling for L1 Nonconvex Optimization

We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function h ◦ F . By classifying points in the domain of the nonsmooth function h into what we call manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current trust region. We motivate this idea through a study of l1...