Scalable multi-group nonnegative spatial factorization for spatial genomics data with cell-type heterogeneity

Spatial transcriptomics (ST) technologies enable the study of gene expression within the spatial context of tissues, providing insights into tissue structure, cellular interactions, and disease progression. However, existing dimension reduction methods often overlook spatial information or struggle to distinguish spatial gene patterns from those driven by cell-type differences, limiting biological interpretability by convolving differences in gene expression patterns with differences in cell-type proportions. To address these challenges, we introduce the scalable multi-group nonnegative spatial factorization (smNSF), a computationally-tractable probabilistic framework that integrates spatial coordinates and cell-type labels into a unified matrix factorization model. By using multi-group Gaussian processes (MGGPs) as priors, our model captures complex spatial variation in a cell-type specific way while enforcing nonnegativity to enhance interpretability. We develop a variational inference framework for MGGPs that supports scalable optimization and improves the numerical stability of smNSF. Across seven spatial transcriptomics datasets spanning diverse technologies and tissues, smNSF recovers sparse, interpretable spatial factors and, through its cell-type conditional posteriors, organizes them into cell-type enriched, cell-type specific, and universal spatial programs that are not apparent from marginal factors alone. Given cell-type labels in ST data, smNSF enables cell-type aware spatial decompositions and supports cell-type conditional posteriors for in silico exploration of relationships between spatial patterns and cellular identity.