The Dirichlet process mixture (DPM) model has been widely used as a Bayesian nonparametric model for clustering. However, the exchangeability assumption of the Dirichlet process is not valid for clustering spatially correlated time series as these data are indexed spatially and temporally. While analyzing spatially correlated time series, correlations between observations at proximal times and locations must be appropriately considered. In this study, we propose a location-dependent DPM model by extending the traditional DPM model for clustering spatially correlated time series. We model the temporal pattern as an infinite mixture of Gaussian processes while considering spatial dependency using a location-dependent Dirichlet process prior over mixture components. This encourages the assignment of observations from proximal locations to the same cluster. By contrast, because mixture atoms for modeling temporal patterns are shared across space, observations with similar temporal patterns can be still grouped together even if they are located far apart. The proposed model also allows the number of clusters to be automatically determined in the clustering procedure. We validate the proposed model using simulated examples. Moreover, in a real case study, we cluster adjacent roads based on their traffic speed patterns that have changed as a result of a traffic accident occurred in Seoul, South Korea.

中文翻译：

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使用位置相关狄利克雷过程混合模型的空间相关时间序列聚类

狄利克雷过程混合 (DPM) 模型已广泛用作聚类的贝叶斯非参数模型。然而，狄利克雷过程的可交换性假设对于空间相关时间序列的聚类无效，因为这些数据在空间和时间上都有索引。在分析空间相关时间序列时，必须适当考虑邻近时间和位置的观测值之间的相关性。在本研究中，我们通过扩展用于聚类空间相关时间序列的传统 DPM 模型，提出了一种位置相关的 DPM 模型。我们将时间模式建模为高斯过程的无限混合，同时使用优先于混合分量的位置相关狄利克雷过程来考虑空间依赖性。这鼓励将来自邻近位置的观测值分配给同一簇。相比之下，由于用于建模时间模式的混合原子是跨空间共享的，因此具有相似时间模式的观测结果仍然可以分组在一起，即使它们相距很远。所提出的模型还允许在聚类过程中自动确定聚类的数量。我们使用模拟示例验证了所提出的模型。此外，在一个真实的案例研究中，我们根据因韩国首尔发生的交通事故而发生变化的交通速度模式对相邻道路进行聚类。