Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single quadratic form and derive general consistency conditions. We reveal that several widely used methods, including Moran's I, are inconsistent, and propose scalable corrections. The resulting test enables robust pattern detection across millions of spatial locations and single-cell lineage-tracing datasets.

翻译：空间模式的检测是科学发现的基础，然而现有方法缺乏统计共识，且应用于大规模空间组学数据集时面临计算障碍。我们通过单一二次型统一了主要方法，并推导出一般一致性条件。研究表明包括莫兰指数在内的多种广泛使用的方法具有不一致性，并提出了可扩展的修正方案。所得检验方法能够在数百万空间位点及单细胞谱系追踪数据集中实现稳健的模式检测。