Contractive Anchor Resolvent Diffusion for Incomplete Multi-View Clustering

Incomplete Multi-View Clustering (IMVC) is affected not only by missing feature values, but also by the degradation of relational structure induced by missing views. Many graph-based approaches either rely on costly data imputation or adopt first-order fusion mechanisms, which can be viewed as shallow low-pass filters with limited spectral selectivity. As a result, they may be insufficient to distinguish latent consensus structure from view-specific structural variations. 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 structural refinement without explicit view imputation. CARD constructs a unified anchor-induced hypergraph from observed sample--anchor relations and derives a high-order resolvent diffusion operator that acts as a rational spectral filter. This operator enhances the relative response of consensus-dominant modes while attenuating view-specific variations. We further derive a compact implicit solver that couples similarity learning and clustering without materializing dense matrices, and provide a conditional local refinement analysis under spectral-gap and local-stability assumptions. Extensive experiments on eight benchmarks, including large-scale datasets, show that CARD achieves competitive performance while scaling linearly in (N) for a fixed anchor budget. The code for our method is publicly available at \url{https://github.com/Whale-Waves/CARD}.

Many real-world datasets describe the same item in several different ways, such as images, text, sensor readings, or other types of features. In practice, some of these descriptions are often missing because of collection failures, privacy limits, or incomplete records. This makes it harder to automatically group similar items together, since the relationships between items can become noisy or broken. This paper proposes CARD, a method for grouping such incomplete multi-source data without trying to guess or recreate the missing information. Instead of filling in missing parts, CARD uses only the information that is actually observed. It builds a compact structure that connects data points to representative anchors, then uses this structure to strengthen reliable relationships and reduce the influence of misleading or view-specific noise. The method is designed to be efficient, so it avoids storing very large pairwise relationship tables and can handle large datasets more easily. Experiments on eight benchmark datasets show that CARD performs competitively or better than existing methods across many missing-data settings, including severe cases where most views are missing. These results suggest that carefully improving the observed relationships between data points can be an effective alternative to reconstructing missing data.