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A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data

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Abstract

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.

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Acknowledgements

The authors would like to thank the creators of different public datasets used in this paper. The authors also thank Dr. Adam Duncan for his contributions in the implementation of a preliminary version of the approach and Dr. Derek Tucker for his contribution in the Python implementation of FAQ algorithm. This research was supported in part by the Grants NSF CDS&E DMS 1953087 and NSF IIS 1955154 to AS, and NSF IIS 1956050 to SS.

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  1. Department of Statistics, Florida State University, Tallahassee, FL, 32306, USA

    Xiaoyang Guo & Anuj Srivastava

  2. Department of Computer Science and Engineering, University of South Florida, Tampa, FL, 33620, USA

    Sudeep Sarkar

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  1. Xiaoyang Guo
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Guo, X., Srivastava, A. & Sarkar, S. A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data. J Math Imaging Vis 63, 735–752 (2021). https://doi.org/10.1007/s10851-021-01027-1

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