Poster: Topic modeling for Spatially Coherent Documents

Topic modeling is a widely used unsupervised method for uncovering latent structure in document corpora by representing each document as a mixture of topics, each defined as a distribution over word frequencies. Originally developed to reduce document representations to low-dimensional latent semantic spaces, topic modeling has been successfully deployed for the analysis of count data in a number of applications, including single cell analysis. Recently, there has been increasing interest in adapting topic models to study cellular microenvironments by exploiting the spatial cell information. Here, documents correspond to microenvironments and words to cell types. By leveraging the frequency of cells in each microenvironment, the goal is to idenity communities of co-abundant cells that share similar patterns of cell interactions. This setting is akin to the incorporation of additional document-level information to traditional topic models. While recent advances have primarily employed Bayesian methods to integrate document metadata for enhanced topic estimation, no theoretical guarantees have been established for general topic modeling with spatially coherent documents. In this work, we adopt a Singular Value Decomposition (SVD)-based approach for topic modeling and view this problem as a spatially-constrained SVD scheme with documents forming a sparse network. We provide a fast iterative SVD algorithm that optimizes for total variation regularization at each step, and derive a high probability bound on its estimation error. It is notable that there is a significant gain by sharing information across spatially coherent documents and that it outperforms existing methods in both speed and error. We complement these findings through synthetic data experiments and also explore its application to multiplexed images of mouse spleen B cells and colorectal tumor cells.