This manuscript studies latent space graph-fused LASSO methods for clustering graphs with multivariate nodal attributes. The framework includes node-specific priors of low-dimensional representations coupled with a neural decoder that bridges the observed attributes with the latent variables. Both structural and attribute information are incorporated for the clustering through a graph-fused LASSO regularization on prior nodal means. The optimization problem is solved via the alternating direction method of multipliers with Langevin dynamics for posterior inference. Simulations on grid and block graphs, together with applications to California county temperatures and Los Angeles traffic data, demonstrate the effectiveness of the proposed method.

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