Generalized multidimensional scaling
Generalized multidimensional scaling (GMDS) is an extension of metric multidimensional scaling, in which the target space in non-Euclidean. In case when the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another.
GMDS is an emerging research direction. Currently, main applications are recognition of deformable objects (e.g. for three-dimensional face recognition) and texture mapping.
References
- Bronstein, A. M, Bronstein, M.M, and Kimmel, R. (2006), Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching, Proc. National Academy of Sciences (PNAS), Vol. 103/5, pp. 1168-1172, January 2006.