SpectralNet is a graph clustering method that uses neural network to find an embedding separates the data. So far it was only used with k-nn graphs, which are usually constructed using distance metric (e.g., Euclidean distance). graphs restrict points have fixed number of neighbors regardless local statistics around them. We proposed new similarity based on random projection trees (rpTrees). Ou...

The paper is concerned with the optimal design problems for the fourth order variational inequalities. Namely, the first order necessary optimality conditions are derived for the class of optimization problems under consideration. The differential stability of metric projection in the Sobolev space HQ{Q) onto the cone of nonnegative elements is considered by Mignot [9]. Mignot derived the form ...

The projection filter is an approximate nonlinear filter based on orthogonal projection in the tangent space of a manifold of densities. The Riemannian metric used is the Fisher information metric. In this paper it is shown that if one uses Gaussian densities the projection filter equals a McShane-Fisk-Stratonovich version of the socalled Assumed Density Filter.

We prove that in a convex metric space (X, d), an existence set K having a lower semi continuous metric projection is a δ-sun and in a complete M -space, a Chebyshev set K with a continuous metric projection is a γ-sun as well as almost convex.