Beyond Scalar Distances: Geometry-Aware Quantum Evidential C-Means via Contrastive Learning

Traditional distance-based clustering methods lack the representational capacity for intricate uncertainty. To address this, evidential c-means (ECM) clustering introduces the concept of credal partition, providing a more flexible and expressive framework for uncertain data modeling. However, ECM fundamentally relies on a nondirectional scalar distance metric, focusing solely on how far samples are from centroids while ignoring their spatial distribution relative to overlapping clusters. To overcome these limitations, we we build upon generalized quantum evidence theory to propose a new method, quantum evidential c-means based on contrastive learning (CL-QECM). It not only integrates a fine-grained contrastive attraction-repulsion mechanism, but also encodes these spatial relationships into a geometry-aware angular representation within the complex credal space. Utilizing a temperature-scaled softmax function, the proposed method explicitly maximizes the similarity of positive pairs and minimizes the similarity of negative pairs in terms of distance. Extensive experiments on twelve benchmark datasets show that CL-QECM outperforms state-of-the-art methods in Purity, NMI, and ARI by up to 7.42%, 3.43%, and 7.30% respectively, exhibiting superior robustness and stability under noise and multi-cluster overlap.