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Title: A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data
Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling. We demonstrate the efficacy of this framework using datasets taken from several problem areas, including letters, biochemical structures, and social networks.
Authors:
; ;
Award ID(s):
1956050
Publication Date:
NSF-PAR ID:
10278120
Journal Name:
Journal of mathematical imaging and vision
Volume:
63
Page Range or eLocation-ID:
735–752
ISSN:
1573-7683
Sponsoring Org:
National Science Foundation
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