Multiscale Covariance Fields, Local Scales, and Shape Transforms
Diego H. Diaz Martinez, Facundo Memoli, Washington Mio
We introduce multiscale covariance fields associated with probability measures on Euclidean space and use them to define local scales at a point and to construct shape transforms. Local scales at x may be interpreted as scales at which key geometric features of data organization around x are revealed. Shape transforms are used to identify points that are most salient in terms of the local-global geometry of a probability distribution, yielding compact geometric summaries of the distribution.