BASIN: Bayesian mAtrix variate normal model with Spatial and sparsIty priors in Non-negative deconvolution

2025-10-17

AI Summary

Spatial transcriptomics data lack cellular resolution, necessitating robust cell-type deconvolution methods. To address this, we propose BASIN—a novel Bayesian nonnegative matrix factorization (NMF) framework operating on matrix-variate distributions. BASIN innovatively incorporates a graph Laplacian prior to explicitly encode spatial neighborhood structure, while enforcing nonnegativity and sparsity constraints on the factor matrices. Posterior inference of cell-type proportions is performed efficiently via Gibbs sampling, enabling principled uncertainty quantification. Extensive evaluations on multiple real-world spatial transcriptomics datasets demonstrate that BASIN consistently outperforms state-of-the-art methods in accuracy, computational efficiency, and robustness to noise and spatial heterogeneity. Theoretical analysis and empirical validation jointly confirm the efficacy and rationality of BASIN’s truncated matrix-normal prior design, which ensures biologically plausible and spatially coherent decomposition.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Data transparency and provenance

Abstract

Spatial transcriptomics allows researchers to visualize and analyze gene expression within the precise location of tissues or cells. It provides spatially resolved gene expression data but often lacks cellular resolution, necessitating cell type deconvolution to infer cellular composition at each spatial location. In this paper we propose BASIN for cell type deconvolution, which models deconvolution as a nonnegative matrix factorization (NMF) problem incorporating graph Laplacian prior. Rather than find a deterministic optima like other recent methods, we propose a matrix variate Bayesian NMF method with nonnegativity and sparsity priors, in which the variables are maintained in their matrix form to derive a more efficient matrix normal posterior. BASIN employs a Gibbs sampler to approximate the posterior distribution of cell type proportions and other parameters, offering a distribution of possible solutions, enhancing robustness and providing inherent uncertainty quantification. The performance of BASIN is evaluated on different spatial transcriptomics datasets and outperforms other deconvolution methods in terms of accuracy and efficiency. The results also show the effect of the incorporated priors and reflect a truncated matrix normal distribution as we expect.

Problem

• Develops Bayesian matrix factorization for spatial transcriptomics deconvolution
• Infers cell type proportions with uncertainty quantification in tissues
• Incorporates spatial and sparsity priors for robust cellular composition analysis

Innovation

• Bayesian matrix variate normal model with priors
• Non-negative matrix factorization with graph Laplacian
• Gibbs sampler for posterior distribution approximation