Contractive Anchor Resolvent Diffusion for Incomplete Multi-View Clustering

Incomplete Multi-View Clustering (IMVC) is fundamentally challenged by structural degradation induced by missing views, rather than the absence of feature values. Existing graph-based approaches either rely on costly data imputation or adopt first-order linear fusion, which acts as a weak low-pass filter and fails to separate latent consensus structure from structural noise. To address this limitation, we reformulate IMVC from a spectral filtering perspective and propose \textbf{C}ontractive \textbf{A}nchor \textbf{R}esolvent \textbf{D}iffusion (\textbf{CARD}), a scalable framework for high-order structural inference without explicit imputation. CARD constructs a unified anchor-induced hypergraph and derives a high-order resolvent diffusion operator that functions as a sharp rational filter to amplify consensus signals while suppressing view-specific noise. We further derive an implicit solver that jointly optimizes similarity learning and clustering without materializing dense matrices, and prove that the resulting process constitutes a local contraction mapping toward the consensus subspace. Extensive experiments on large-scale benchmarks demonstrate that CARD consistently outperforms state-of-the-art IMVC methods with linear complexity. The code for our method is publicly available at \url{https://anonymous.4open.science/r/CARD-8CB1}.