Incomplete Gromov-Wasserstein Alignment for Multi-View Clustering

Incomplete multi-view clustering (IMVC) struggles with heterogeneous feature spaces and severe instance missingness. Current methods typically project disparate views into a shared Euclidean space and rely on static graphs to preserve local structures. However, these point-to-point embeddings ignore intrinsic metric discrepancies across modalities and suffer from topological distortion when samples are missing. To address this, we propose Incomplete Gromov-Wasserstein Alignment (IGWA), a novel optimal transport framework for IMVC. IGWA abandons forced Euclidean consensus representations; instead, it directly couples heterogeneous intra-view metric spaces by learning a probabilistic transport plan. Building on established partial Gromov–Wasserstein transport, we incorporate view-specific partial couplings into a learnable global consensus framework, allowing reliable structural mass to be aligned without explicit data imputation. By matching intra-view distance matrices rather than raw features, IGWA preserves geometric invariants and maintains robustness against missing nodes. Furthermore, we establish relabeling invariance and balanced recovery of the partial alignment, together with uniqueness, boundedness, and perturbation stability of the consensus update under fixed transport plans and view weights. Extensive experiments on diverse benchmarks demonstrate that IGWA consistently outperforms State-of-The-Art IMVC methods.