Connectionists: Robust Manifold Unfolding with Kernel Regularization

[Grace Wahba]

  Esteemed colleagues:

  Robust Manifold Unfolding with Kernel Regularization
              Fan Lu, Yi Lin and Grace Wahba
                 TR1108 October, 2005
 University of Wisconsin Madison Statistics Dept TR 1108.

 http://www.stat.wisc.edu/~wahba   -> TRLIST or
 http://www.stat.wisc.edu/~wahba/ftp1/tr1108.pdf

                      Abstract
We describe a robust method to unfold a low-dimensional manifold embedded in
high-dimensional Euclidean space based on only pairwise distance information
(possibly noisy) from the sampled data on the manifold. Our method is derived
as one special extension of the recently developed framework called Kernel
Regularization, ( http://www.pnas.org/cgi/content/full/102/35/12332 ) 
which is originally designed to extract information in the form of a 
positive definite kernel matrix from possibly crude, noisy, incomplete,
inconsistent dissimilarity information between pairs of objects. The special
formulation is transformed into an optimization problem that can be solved
globally and efficiently using modern convex cone programming techniques.
The geometric interpretation of our method will be discussed. Relationships
to other methods for this problem are noted.