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.