Thursday, October 10, 2013 - 3:15pm - 4:05pm
Elizabeth Munch (University of Minnesota, Twin Cities)
Recent progress has shown that the abstract space of persistence diagrams is Polish, and found necessary and sufficient conditions for a set to be compact.
This also allowed for the definition of Frechet means, a construction which is possible for any metric space. Since the Frechet mean is a set, not an element, there were no guarantees that this set was non-empty, however Mileyko et al showed that for well behaved distributions, the Frechet mean is, in fact, non-empty.
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