Bayesian Nonparametric Joint Mixture Model for Clustering Spatially Correlated Time Series

We develop a Bayesian nonparametric joint mixture model for clustering spatially correlated time series based on both spatial and temporal similarities. In the temporal perspective, the pattern of a time series is flexibly modeled as a mixture of Gaussian processes, with a Dirichlet process (DP) prior over mixture components. In the spatial perspective, the spatial location is incorporated as a feature for clustering, like a time series being incorporated as a feature. Namely, we model the spatial distribution of each cluster as a DP Gaussian mixture density. For the proposed model, the number of clusters does not need to be specified in advance, but rather is automatically determined during the clustering procedure. Moreover, the spatial distribution of each cluster can be flexibly modeled with multiple modes, without determining the number of modes or specifying spatial neighborhood structures in advance. Variational inference is employed for the efficient posterior computation of the proposed model. We validate the proposed model using simulated and real-data examples. Supplementary materials for the article are available online.

本研究构建了一种基于空间与时间相似性的贝叶斯非参数联合混合模型，用于对空间相关时间序列开展聚类分析。从时间维度来看，我们将时间序列的模式灵活建模为高斯过程（Gaussian Processes）的混合，并为混合分量赋予狄利克雷过程（Dirichlet Process, DP）先验。从空间维度来看，我们将空间位置作为聚类特征纳入模型，正如将时间序列作为聚类特征一般。具体而言，我们将每个聚类的空间分布建模为狄利克雷过程高斯混合密度。针对所提出的模型，无需预先指定聚类数目，而是可在聚类过程中自动确定。此外，每个聚类的空间分布可灵活建模为多峰形式，无需预先确定峰的数量，也无需指定空间邻域结构。本研究采用变分推断（Variational Inference）完成所提模型的高效后验计算。我们通过模拟数据与真实数据示例对所提模型进行了验证。本文的补充材料可在线获取。