Optimal Transport-Guided Geometric Contrastive Learning for Attributed Graph Clustering

Deep attributed graph clustering learns discriminative node representations by fusing node attributes and topology without label supervision, but two issues persist. Propagation operators — fixed spectral convolutions or learned attention scores — aggregate neighbor features by topology alone or by a metrically ungrounded scorer, injecting noise whenever a neighbor is uninformative for a node's cluster identity. The contrastive objectives typically used to sharpen these representations rely on stochastic graph augmentation and large negative pools, both heuristic, costly, and prone to distorting graph semantics through arbitrary perturbation. We introduce OT-GeoCL, which resolves both issues with a single entropic optimal transport coupling. Node attributes are mapped onto the unit hypersphere, and a sparse Sinkhorn coupling, computed from the induced geometric cost and restricted to the graph's edges, serves simultaneously as a geometry-adaptive propagation operator that down-weights uninformative neighbors by construction, and as the soft positive-pair weighting of a contrastive loss requiring neither augmentation nor heuristic negative sampling. We prove the resulting objective admits an exact, non-asymptotic alignment-uniformity decomposition, belongs to the InfoNCE family with explicit limiting cases, and resists representation collapse via spherical potential theory — guarantees unavailable to heavier, heuristically assembled pipelines. Across 12 widely used attributed graph clustering benchmarks spanning citation, co-purchase, and co-authorship networks, OT-GeoCL outperforms fourteen representative generative, contrastive, and multi-task self-supervised baselines.