Generalized multidimensional scaling

Generalized multidimensional scaling (GMDS) is an extension of metric <a href="/facts/Multidimensional_scaling/0L4klSl6">multidimensional scaling</a>, in which the target space is non-Euclidean. 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 <a href="/facts/Three-dimensional_face_recognition/mMj9Ivo4">three-dimensional face recognition</a>) and texture mapping.

<ul><li>Bronstein AM, Bronstein MM, Kimmel R (January 2006). <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1360551">"Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching"</a>. Proc. Natl. Acad. Sci. U.S.A. 103 (5): 1168–72. <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2006PNAS..103.1168B">2006PNAS..103.1168B</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1073%2Fpnas.0508601103">10.1073/pnas.0508601103</a>. <a href="/facts/PMC_(identifier)/dX1zMt71">PMC</a> <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1360551">1360551</a>. <a href="/facts/PMID_(identifier)/JlHAvMHt">PMID</a> <a href="https://pubmed.ncbi.nlm.nih.gov/16432211">16432211</a>.</li></ul>

Generalized multidimensional scaling open-in-new

Generalized multidimensional scaling