This manuscript studies nodal clustering in graphs having multivariate attributes at each node. The framework includes node-specific priors for low-dimensional representations, coupled with a neural decoder that bridges observed attributes with latent variables. Structural and attribute information are incorporated through a graph-fused LASSO regularization on the prior means, promoting nodal clustering. The optimization problem is solved via alternating direction method of multipliers, with Langevin dynamics for posterior inference. Simulation studies on grid graphs, and applications to real data with complex settings, demonstrate the effectiveness of the proposed clustering method.

翻译：本文研究具有多元属性的图中节点聚类问题。该框架包含用于低维表示的节点特定先验，以及连接观测属性与潜在变量的神经解码器。通过在图融合LASSO正则化中对先验均值施加约束，融合了结构和属性信息，从而促进节点聚类。采用交替方向乘子法求解优化问题，并利用朗之万动力学进行后验推断。在网格图上的仿真实验以及复杂真实数据应用表明，所提出的聚类方法具有有效性。