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Min."],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In recent years, Graph Neural Network (GNN)\u2013based anomaly detection has been widely applied to identify fraudulent or abnormal behaviors in complex relational ecosystems, such as e-commerce platforms and online review networks. Despite their popularity, conventional GNNs often struggle to generalize in these settings due to noisy and imbalanced data, limited supervision, and the implicit assumption of homogeneity. However, it is well known that the presence of anomalies typically disrupts this homogeneity and leads to a heterophilic eigenvalue distribution, which further degrades the performance of standard GNN architectures in the anomaly detection context. To address these limitations, we introduce\n                    <jats:sc>CaRgo<\/jats:sc>\n                    , a\n                    <jats:bold>C<\/jats:bold>\n                    onstr\n                    <jats:bold>a<\/jats:bold>\n                    stive\n                    <jats:bold>R<\/jats:bold>\n                    epresentation Learnin\n                    <jats:bold>g<\/jats:bold>\n                    framework for An\n                    <jats:bold>o<\/jats:bold>\n                    maly Detection in Multi-Relational Graphs. The proposed model integrates contrastive learning with multi-relational message passing to enhance both the robustness and discriminative power of learned representations. Specifically, we use a relation-aware polynomial convolution mechanism to capture heterogeneous dependencies across different entity types, and we formulate a self-supervised contrastive objective that promotes consistency in node embeddings across perturbed views of the graph. By jointly optimizing supervised and contrastive losses,\n                    <jats:sc>CaRgo<\/jats:sc>\n                    learns more informative and stable representations, even in scenarios with limited or noisy labels. Extensive experiments on two real-world datasets, Amazon and Yelp, demonstrate that our approach outperforms state-of-the-art baselines. These results highlight the effectiveness of contrastive learning as a strong inductive bias for detecting complex anomalous patterns in multi-relational graphs.\n                  <\/jats:p>","DOI":"10.1007\/s13278-026-01612-5","type":"journal-article","created":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T11:09:59Z","timestamp":1781780999000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["CaRgo: contrastive representation learning for anomaly detection in multi-relational graphs"],"prefix":"10.1007","volume":"16","author":[{"given":"Melike","family":"Yildiz Aktas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mustafa","family":"Coskun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-Tien","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,18]]},"reference":[{"key":"1612_CR1","doi-asserted-by":"crossref","unstructured":"Aktas MY, Alkulaib L, Lu C-T (2023) Unimhe: Unified multi hyperedge prediction a case study on crime dataset. 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