This manuscript studies nodal clustering in graphs having a time series at each node. The proposed framework includes priors for low-dimensional representations and a decoder that bridges latent representations with time series. Addressing the limitation that the evolution of nodal attributes is often overlooked, temporal and structural patterns are fused into low-dimensional representations to facilitate clustering. Parameters are learned via maximum approximate likelihood, with a graph-fused LASSO regularization imposed on prior parameters. The optimization problem is solved via alternating direction method of multipliers; Langevin dynamics are employed for posterior inference. Simulation studies on block and grid graphs with autoregressive dynamics, and applications to California county temperatures and a word co-occurrence network demonstrate the effectiveness of the proposed clustering method.

翻译：本文研究在每个节点具有时间序列的图结构中的节点聚类问题。所提出的框架包含低维表示的先验分布，以及连接潜在表示与时间序列的解码器。针对节点属性演化常被忽视的局限性，本研究将时间模式与结构模式融合至低维表示中以促进聚类。参数通过近似最大似然估计进行学习，并对先验参数施加图融合LASSO正则化。优化问题通过交替方向乘子法求解，并采用朗之万动力学进行后验推断。在具有自回归动态特性的块图与网格图上的仿真研究，以及对加利福尼亚郡县温度数据和词语共现网络的实际应用，均验证了所提出聚类方法的有效性。