Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one `best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a consensus matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name.

翻译：在集成聚类文献中，已开发出多种方法用于结合无监督聚类的多组结果进行推断。从多个候选聚类模型中选择一个“最佳”模型并报告其结果的方法，通常忽略了模型选择带来的不确定性，导致推断结果对所选模型及其参数敏感。贝叶斯模型平均（BMA）是一种流行的跨模型结果结合方法，在此设置下具有若干吸引人的优势，包括对合并聚类结构的概率解释以及基于模型不确定性的量化。本文介绍了clusterBMA，这是一种能够跨多个无监督聚类算法结果实现加权模型平均的方法。我们利用聚类内部验证准则来近似后验模型概率，用于对各模型结果进行加权。通过一个表示跨模型聚类解加权平均的共识矩阵，我们应用对称单纯形矩阵分解来计算最终的概率聚类分配。除了在模拟数据上优于其他集成聚类方法外，clusterBMA还提供了独特功能，包括平均聚类的概率分配、结合“硬”和“软”聚类算法的分配概率，以及测量平均聚类分配中基于模型的不确定性。该方法已在同名R软件包中实现。