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Linear-Projection Diffusion on Smooth Euclidean Submanifolds

Summary: Linear-Projection Diffusion on Smooth
Euclidean Submanifolds
Guy Wolf Amir Averbuch
School of Computer Science
Tel Aviv University, Tel Aviv 69978, Israel
April 26, 2011
To process massive high -dimensional datasets, we utilize the un-
derlying assumption that data on manifold is approximately linear in
sufficiently small patches (or neighborhoods of points) that are sam-
pled with sufficient density from the manifold. Under this assumption,
each patch can be represented (up to a small approximation error) by
a tangent space of the manifold in its area and the tangential point of
this tangent space.
We extend previously obtained results[1] for the finite construction
of a linear-projection diffusion (LPD) super-kernel by exploring its
properties when it becomes continuous. Specifically, its infinitesimal
generator and the stochastic process defined by it are explored. We
show that the resulting infinitesimal generator of this super-kernel con-
verges to a natural extension of the original diffusion operator from


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences