发表机构
Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对现有函数聚类方法的局限性，提出一种结合狄利克雷过程先验、自适应平滑度控制与灵活协方差建模的自适应贝叶斯函数聚类方法，采用变分推断提升计算效率，用于处理带结构化曲线内依赖的函数数据聚类。
AI 中文摘要
函数聚类是识别函数数据中潜在异质性的重要工具，已广泛应用于多个科学领域。然而，许多现有方法并非完全自适应，它们可能需要预先指定聚类数量，且无法自动控制基础函数的平滑度，还通常假设误差独立同分布，从而忽略了曲线内的额外依赖关系。我们提出一种完全自适应的贝叶斯函数聚类方法，通过狄利克雷过程先验、自适应平滑度控制和灵活协方差建模来解决这些限制。为实现计算可扩展性，该方法采用变分推断作为马尔可夫链蒙特卡罗的高效替代方案。这些特性共同构成了一个统一的贝叶斯框架，用于在存在结构化曲线内依赖的情况下进行函数聚类和聚类特异性均值函数估计。
英文摘要
Functional clustering is an important tool for identifying latent heterogeneity in functional data and has been widely applied across various scientific fields. However, many existing methods are not fully adaptive, as they may require the number of clusters to be prespecified and may lack automatic control over the smoothness of the underlying functions. They also commonly assume independent and identically distributed errors, thereby overlooking additional within-curve dependence. We propose a fully adaptive Bayesian procedure for functional clustering that addresses these limitations through Dirichlet process priors, adaptive smoothness control, and flexible covariance modeling. For computational scalability, the proposed method employs variational inference as an efficient alternative to Markov chain Monte Carlo. Together, these features provide a unified Bayesian framework for functional clustering and cluster-specific mean function estimation in the presence of structured within-curve dependence.
