This manuscript studies nodal clustering in graphs having a time series at each node. The framework includes priors for low-dimensional representations and a decoder that bridges the latent representations and time series. The structural and temporal patterns are fused into representations that facilitate clustering, addressing the limitation that the evolution of nodal attributes is often overlooked. 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 book word co-occurrence network demonstrate the effectiveness of the proposed method.

翻译：本文研究了在图中每个节点上具有时间序列的节点聚类问题。该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。结构模式与时间模式被融合到表示中，以促进聚类，从而解决了节点属性演化常被忽视的局限性。参数通过最大近似似然法学习，并在先验参数上施加图融合LASSO正则化。优化问题通过交替方向乘子法求解；后验推断采用朗之万动力学方法。在具有自回归动态的块图与网格图上的仿真研究，以及在加利福尼亚县温度数据和书籍词汇共现网络中的应用，均证明了所提方法的有效性。