A Variational Principle for Model-Based Morphing
Abstract
Given a multidimensional data set and a model of its density, we consider how to define the optimal interpolation between two points. This is done by assigning a cost to each path through space, based on two competing goals-one to interpolate through regions of high density, the other to minimize arc length. From this path functional, we derive the Euler-Lagrange equations for extremal motionj given two points, the desired interpolation is found by solv(cid:173) ing a boundary value problem. We show that this interpolation can be done efficiently, in high dimensions, for Gaussian, Dirichlet, and mixture models.
Cite
Text
Saul and Jordan. "A Variational Principle for Model-Based Morphing." Neural Information Processing Systems, 1996.Markdown
[Saul and Jordan. "A Variational Principle for Model-Based Morphing." Neural Information Processing Systems, 1996.](https://mlanthology.org/neurips/1996/saul1996neurips-variational/)BibTeX
@inproceedings{saul1996neurips-variational,
title = {{A Variational Principle for Model-Based Morphing}},
author = {Saul, Lawrence K. and Jordan, Michael I.},
booktitle = {Neural Information Processing Systems},
year = {1996},
pages = {267-273},
url = {https://mlanthology.org/neurips/1996/saul1996neurips-variational/}
}