In graph motivated learning, label propagation largely depends on data affinity represented as edges between connected points. The assignment implicitly assumes even distribution of the manifold. This assumption may not hold and lead to inaccurate metric due drift towards high-density regions. affected heat kernel based with a globally fixed Parzen window either discards genuine neighbors or fo...

We study the manifold of all metrics with the fixed volume form on a compact Riemannian manifold of dimension ≥ 3. We compute the characteristic function for the L (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and nontrivial examples of higher order Osserman manifolds. Subject Classification: 53B20. PACS numbers: 0240, 0...

This paper proposes a novel online domain-shift appearance learning and object tracking scheme on a Riemannian manifold for visual and infrared videos, especially for video scenarios containing large deformable objects with fast out-of-plane pose changes that could be accompanied by partial occlusions. Although Riemannian manifolds and covariance descriptors are promising for visual object trac...

where Rij is the Ricci curvature tensor of the metric and R is its scalar curvature. This equation tells us how the metric tensor gij (i.e. the field mediating the gravitation) is obeying to constraints imposed by the energy-momentum tensor Tij , which encodes informations about the distribution of energy and momentum in spacetime. For simplicity we will assume in the following that Tij = 0, i....