Graph-Structured Topic Modeling for Documents with Spatial or Covariate Dependencies

We address the challenge of incorporating document-level metadata into topic modeling to improve topic mixture estimation. To overcome the computational complexity and lack of theoretical guarantees in existing Bayesian methods, we extend probabilistic latent semantic indexing (pLSI), a frequentist framework for topic modeling, by incorporating document-level covariates or known similarities between documents through a graph formalism. Modeling documents as nodes and edges denoting similarities, we propose a new estimator based on a fast graph-regularized iterative singular value decomposition (SVD) that encourages similar documents to share similar topic mixture proportions. We characterize the estimation error of our proposed method by deriving high-probability bounds and develop a specialized cross-validation method to optimize our regularization parameters. We validate our model through comprehensive experiments on synthetic datasets and three real-world corpora, demonstrating improved performance and faster inference compared to existing Bayesian methods.