A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data
This work addresses the need for generative modeling and statistical tools in graphical data analysis, which is incremental as it builds on existing methods for graph matching and comparison.
The paper tackles the problem of developing statistical analyses for graphical data by introducing a quotient space formulation to compute mathematical representations and metrics for graphs, resulting in efficient algorithms for tools like principal component analysis and statistical testing, demonstrated on datasets including letters, biochemical structures, and social networks.
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.