Spatial transcriptomics is a rapidly growing technique that captures gene expression together with spatial coordinates in intact tissue sections, enabling in situ mapping of transcriptional activity. This technology offers unprecedented opportunities to study tissue heterogeneity and spatial gene expression patterns. Uncovering the associations between spatially variable gene modules and spot types can advance our understanding of pathological mechanisms. However, rigorous statistical methods that exploit spatial information to achieve spatially coherent co-clustering of spots and genes are still lacking, and theoretical investigations in this direction remain limited. We propose a fused spatial latent block model (F-SpLBM). Our model uses the LBM to uncover co-expression patterns between spots and genes, penalized fusion to automatically determine the number of co-clusters, and the Potts model to incorporate spatial information. We establish that the fusion-based procedure recovers the true block structure with the misclassification rate converging at a super-polynomial rate. We also prove asymptotic normality of the parameter estimators and quantify the accuracy gain from spatial smoothing. Simulations and real-data analyses demonstrate that F-SpLBM yields spatially coherent and biologically interpretable clustering results.

翻译：空间转录组学是一种快速发展的技术，可在完整组织切片中同时捕获基因表达与空间坐标，从而实现转录活性的原位定位。该技术为研究组织异质性和空间基因表达模式提供了前所未有的机遇。揭示空间可变基因模块与斑点类型之间的关联，能够促进我们对病理机制的理解。然而，目前仍缺乏利用空间信息实现斑点和基因空间一致性共聚的严谨统计方法，且该方向的理论研究较为有限。我们提出一种融合空间潜在块模型（F-SpLBM）。该模型采用LBM揭示斑点与基因间的共表达模式，通过惩罚融合自动确定共聚类数量，并利用Potts模型整合空间信息。我们证明基于融合的方法能以超多项式收敛速率恢复真实块结构，同时验证参数估计量的渐近正态性，并量化空间平滑带来的精度增益。模拟实验与真实数据分析表明，F-SpLBM能够产生空间一致且具有生物学可解释性的聚类结果。