Abstract
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.
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Martinez, D.H.D., Mémoli, F., Mio, W. (2013). Multiscale Covariance Fields, Local Scales, and Shape Transforms. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_89
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DOI: https://doi.org/10.1007/978-3-642-40020-9_89
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40019-3
Online ISBN: 978-3-642-40020-9
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