Rule-graph alignment via optimal transport for weakly supervised anomaly detection on transaction graphs

Abstract Transaction-graph anomaly detection is challenging because high-quality labels require costly expert investigation. Weakly supervised methods often use limited labels, heuristic rules, or expert knowledge to generate pseudo-labels for unlabeled transactions. Existing methods usually treat rules as flat labeling functions, overlooking both the graph-structured dependencies in transaction behaviors and the complete-path grouping structure of rule paths. They also ignore the mismatch between discrete rules and continuous transaction embeddings, leading to noisy pseudo-labels and error propagation. Motivated by these limitations, we propose a weakly supervised framework that integrates rule-structure encoding with cross-branch contrastive learning (CCL). Our model consists of both a rule branch and a data branch. In the rule branch, an adaptive-depth decision tree is trained on the available labeled training data. Transactions following the same complete decision path form a Rule-Graph group, which is encoded using a graph neural network (GNN). In parallel, the data branch encodes transaction features using a feature encoder. To align the two spaces, we employ optimal transport (OT), which transfers semantic rule knowledge into data representations and produces pseudo-labels for unlabeled samples. CCL then regularizes the OT-induced positive and negative pairs by pulling semantically consistent representations together and separating inconsistent ones. This improves minority-class ranking and can improve pseudo-label precision, although the direct pseudo-label benefit is dataset dependent. Experiments on four datasets demonstrate that the proposed framework achieves strong and competitive performance across diverse graph anomaly detection settings. However, its advantage is more limited in the original-feature Libra Bank setting, characterized by extreme class imbalance and strong feature–label dependence.