We introduce the notion of multiscale covariance tensor fields associated with a probability measure on Euclidean space and use these fields 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 the data organization around x are revealed. Shape transforms are employed to identify points that are most salient in terms of the local-global shape of a probability distribution, yielding a compact summary of the geometry of the distribution. © 2013 Springer-Verlag.
CITATION STYLE
Martinez, D. H. D., Mémoli, F., & Mio, W. (2013). Multiscale covariance fields, local scales, and shape transforms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8085 LNCS, pp. 794–801). https://doi.org/10.1007/978-3-642-40020-9_89
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