One-Step Consistency-aware Graph Dictionary Learning for Incomplete Multi-View Clustering

Missing samples may degrade the clustering performance of incomplete multiview clustering (IMVC), where one-step graph-based methods show great potential. However, existing graph learning methods for IMVC typically fail to exploit consistent and complementary information simultaneously at the graph embedding level. Moreover, they often impose low-rank constraints on high-dimensional affinity tensors with high computational complexity. To this end, we propose One-Step Consistency-aware Graph Dictionary Learning (OCGDL), which employs a partially shared graph dictionary to capture both consistency and complementarity simultaneously from the similarity graph obtained from the incomplete multiview data. We first decompose each partially observed similarity graph into shared and view-specific atoms under self-orthogonality and orthogonal-complement constraints, while a missing-indicator mask confines reconstruction to observed samples. Subsequently, we relax the strict constraint on decomposed graph features by considering graph features as dictionary atoms for affinity reconstruction, and row-wise ${\ell }_{2,1}$ coefficients encourage differentiated atom selection across views. Furthermore, we employ the tensor nuclear norm on the concatenated multiview full graph dictionary tensor of size $k\times V\times n$, which can effectively reduce computational complexity and also encourage high-order cross-view correlations at the embedding level. Discrete cluster indicators are obtained directly in the same objective via spectral rotation with adaptive view weights, forming one-step clustering. Extensive experiments on six benchmark multiview datasets validate the effectiveness of OCGDL under various view missing ratios.