Generative AI and Topological Data Analysis of Longitudinal Panel Data

This article constructs an approach to analyzing longitudinal panel data which combines topological data analysis (TDA) and generative AI applied to graph neural networks (GNNs). TDA is deployed to identify and analyze unobserved topological heterogeneities of a dataset. TDA-extracted information is quantified into a set of measures, called functional principal components. These measures are used to analyze the data in four ways. First, the measures are construed as moderators of the data and their statistical effects are estimated through a Bayesian framework. Second, the measures are used as factors to classify the data into topological classes using generative AI applied to GNNs constructed by transforming the data into graphs. The classification uncovers patterns in the data which are otherwise not accessible through statistical approaches. Third, the measures are used as factors that condition the extraction of latent variables of the data through a deployment of a generative AI model. Fourth, the measures are used as labels for classifying the graphs into classes used to offer a GNN-based effective dimensionality reduction of the original data. The article uses a portion of the militarized international disputes (MIDs) dataset (from 1946 to 2010) as a running example to briefly illustrate its ideas and steps.