Decoder-only Clustering in Graphs with Dynamic Attributes
Yik Lun Kei, Oscar Hernan Madrid Padilla, Rebecca Killick, James Wilson, Xi Chen, Robert Lund
TL;DR
The paper addresses clustering in graphs where each node exhibits a dynamic time series. It proposes a decoder-only latent-space model that assigns node-specific latent means $\bm{\mu}_i$ to guide clustering via a shared neural decoder $\bm{h}_{\bm{\phi}}(\bm{Z}_i)$, and enforces structural coherence with a graph-fused LASSO penalty across edges. Learning proceeds via ADMM on a penalized likelihood, with Langevin dynamics used to approximate posterior expectations for $\bm{Z}_i$, and clustering is performed with $k$-means on the learned priors $\hat{\bm{\mu}}_i$ after selecting the regularization parameter $\lambda$ by cross-validation. The approach is demonstrated on simulations and real data (California temperatures and a word co-occurrence network), showing superior clustering by jointly leveraging temporal dynamics and graph structure and illustrating its practical value for identifying coherent regions and linguistic patterns.
Abstract
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.