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David Dreisigmeyer and Michael Kirby (2007)
A Pseudo-Isometric Embedding Algorithm
submitted.
We present a newWhitney-like algorithm for finding a low-dimensional pseudoisometric
embedding of a sampled Riemannian manifold. Tangent spaces on the
manifold are estimated from the data and then projected using a criterion that
ensures optimal smoothness of the inverse. This short projection is not isometric
but can be made to be approximately isometric by determining an appropriate global
lengthening transformation in the embedded space. We illustrate the application
of this algorithm on numerically obtained solutions of the Kuramoto-Sivashinksy
partial differential equation.
LA-UR-06-3495
A Basic Course in Optimization