Averages of Unlabeled Networks: Geometric Characterization and Asymptotic Behavior
作者： Eric Kolaczyk , Lizhen Lin , Steven Rosenberg , Jackson Walters
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摘要: It is becoming increasingly common to see large collections of network data objects -- that is, sets in which a viewed as fundamental unit observation. As result, there pressing need develop network-based analogues even many the most basic tools already standard for scalar and vector data. In this paper, our focus on averages unlabeled, undirected networks with edge weights. Specifically, we (i) characterize certain notion space all such networks, (ii) describe key topological geometric properties relevant doing probability statistics thereupon, (iii) use these establish asymptotic behavior generalized an empirical mean under sampling from distribution supported space. Our results rely combination geometry, theory, statistical shape analysis. particular, lack vertex labeling necessitates working quotient modding out permutations labels. This nontrivial geometry unlabeled turn found have important implications types probabilistic may be obtained techniques needed obtain them.
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