比利时vs摩洛哥足彩
,
university of california san diego
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data science seminar
facundo memoli
classical multidimensional scaling of metric measure spaces
abstract:
we study a generalization of the classical multidimensional scaling procedure (cmds) to the setting of general metric measure spaces which can be seen as natural 'continuous limits' of finite data sets. we identify certain crucial spectral properties of the generalized cmds operator thus providing a natural and rigorous formulation of cmds in this setting. furthermore, we characterize the cmds output of several continuous exemplar metric measures spaces such as high dimensional spheres and tori (both with their geodesic distance). in particular, the case of spheres (with geodesic distance) requires that we establish that its cmds operator is trace class, a condition which is natural in the context when the cmds operator has infinite rank. finally, we establish the stability of the generalized cmds method with respect to the gromov-wasserstein distance.
may 17, 2022
11:00 am
sdsc e230
https://ucsd.zoom.us/j/93593146777
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