Unified Grassmann Manifold-Based Completion and Alignment for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) tackles the problem of effectively combining complementary yet incomplete data from multiple views to improve clustering results. Conventional IMVC techniques typically focus on either imputing missing entries and constructing separate similarity graphs for each view to derive a unified partition matrix or directly learning a shared representation via matrix factorization. Nevertheless, these methods often fall short in struggling with insufficient mining of geometric information in the Euclidean space, which may introduce noise and redundant information—particularly when handling data with significant missing rates. To overcome this limitation, we introduce Unified Grassmann Manifold-Based Completion and Alignment (UGMCA), a novel approach for IMVC. UGMCA integrates three essential processes: (1) completing missing entries in view-specific partition matrices, (2) aligning these matrices on the Grassmann manifold, and (3) learning adaptive view-specific graphs. Unlike traditional Euclidean-based methods, UGMCA treats multiple partition matrices as the basis of an element on Grassmann manifold, leveraging manifold geometry for more robust integration. By formulating a low-rank tensor learning framework on the Grassmann manifold, UGMCA effectively captures intricate, nonlinear structures inherent in incomplete multi-view data, thereby enhancing clustering accuracy. Extensive experiments on benchmark datasets confirm that UGMCA outperforms existing state-of-the-art methods in terms of clustering performance.