文章基本信息

标题：Probabilistic Fréchet means for time varying persistence diagrams
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作者：Elizabeth Munch ; Katharine Turner ; Paul Bendich 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2015
卷号：9
期号：1
页码：1173-1204
DOI：10.1214/15-EJS1030
语种：English
出版社：Institute of Mathematical Statistics
摘要：In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in $(\mathcal{D}_{p},W_{p})$, the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards.
关键词：Topological data analysis;Fr´echet mean;time varying data.