Adaptive multi-view fuzzy clustering via structure-aware high-order graph learning

Multi-View Fuzzy Clustering (MVFC) is a powerful paradigm for modeling ambiguity and uncertainty in complex multi-view data through flexible membership assignments. However, most existing MVFC methods determine sample memberships primarily based on global sample-centroid distances, largely overlooking the intrinsic local manifold structure and becoming sensitive to noise. Moreover, they often lack an effective mechanism to adaptively weight the contributions of different views. To address these limitations, this paper proposes an Adaptive Multi-view Fuzzy Clustering framework via Structure-aware High-order Graph Learning (AMFC-SHGL). The proposed AMFC-SHGL treats degree information derived from high-order graphs as the structural importance measure and embeds it into the fuzzy objective function, enabling the membership matrix learning to jointly consider both global centroid proximity and local structural connectivity. By embedding high-order structural information to guide the fuzzy decision-making process, the proposed AMFC-SHGL effectively enhances the clustering stability. Furthermore, an adaptive weighting strategy is introduced to automatically identify the importance of each view according to its clustering reliability, facilitating an effective fusion of complementary and consistent information. Additionally, an efficient alternating optimization algorithm with guaranteed convergence to a stationary point and linear computational complexity is developed to solve the proposed AMFC-SHGL. Moreover, AMFC-SHGL is robust to graph-order selection, with a fixed second-order graph achieving competitive performance across all datasets. Extensive experiments conducted on eight real-world multi-view datasets demonstrate that AMFC-SHGL achieves average relative improvements of 5.23% in ACC, 0.73% in NMI, 10.94% in ARI, and 6.82% in F-score over the best-performing baseline methods, confirming its effectiveness in leveraging multi-view data.