Principal coordinates analysis (PCoA) is a standard exploratory tool for microbiome beta-diversity studies, but its axes are defined by pairwise dissimilarities and therefore do not directly identify the taxa driving an ordination. We propose Bayesian sparse principal coordinates analysis (BSPCoA), a post hoc framework that approximates the leading principal coordinates by a sparse linear surrogate in the observed taxa. A delta-tolerance diagnostic quantifies the discrepancy between the classical ordination and its best linear surrogate, clarifying when taxon-level interpretation is well supported. We place three-parameter beta normal global-local priors on the surrogate coefficients to induce row sparsity, obtain posterior uncertainty, and select influential taxa. The method reduces to sparse principal component analysis under Euclidean distance, while remaining applicable to ecologically meaningful dissimilarities such as Bray--Curtis and Hellinger distances. We conduct simulation studies to demonstrate that BSPCoA provides an approximately linear representation of the dominant ordination geometry while enhancing interpretability in sparse microbiome settings. In the Hadza gut microbiome data, the method produces an ordination close to that of classical PCoA while highlighting a parsimonious set of taxa associated with seasonal variation.

翻译：主坐标分析（PCoA）是微生物组β多样性研究的标准探索性工具，但其坐标轴由成对相异性定义，因此无法直接识别驱动排序的分类单元。我们提出贝叶斯稀疏主坐标分析（BSPCoA），这是一种后验框架，通过观察到的分类单元中的稀疏线性替代项来近似主导主坐标。δ-容差诊断指标量化了经典排序与其最优线性替代项之间的差异，从而明确分类单元层面解释的有效性。我们在替代系数上设置三参数贝塔正态全局-局部先验以诱导行稀疏性、获取后验不确定性并筛选具有影响力的分类单元。该方法在欧氏距离下退化为稀疏主成分分析，同时仍适用于生态学意义的相异性指标（如Bray-Curtis和Hellinger距离）。通过模拟研究证明，BSPCoA能在保持主导排序几何结构近似线性的同时，增强稀疏微生物组场景下的可解释性。在哈扎族肠道微生物组数据中，该方法在生成与经典PCoA高度相近排序图的同时，突出显示了与季节变化相关的简约分类单元集合。