Robust geo-sparse and graph-fusion tensor learning for incomplete multi-view clustering

Incomplete multi-view clustering (IMC) arises in many real-world scenarios with missing views, in which the available views provide complementary information for clustering. A key challenge is to recover reliable similarity structure from incomplete multi-view observations under low paired rates (i.e., high missing rates). In this study, we propose a tensor learning framework, termed Robust Geo-Sparse and Graph-Fusion Tensor Learning (RG²F-TL), which jointly leverages within-view structural regularities and cross-view complementarity to infer a more reliable similarity matrix. Specifically, RG²F-TL integrates a Geometry-Conforming Sparse Gradient (GCSG) prior with a graph fusion strategy on a third-order tensor constructed by stacking view-specific similarity matrices. The sparse gradient prior promotes block-sparse and piecewise-smooth patterns along mode-1 and mode-2, while encouraging cross-view consistency along mode-3. To model the prior, we use a Laplace scale mixture (LSM) formulation, supported by distribution-fitting results on real-world datasets. Additionally, we employ joint spectral embedding to fuse view-specific graphs into a unified representation for clustering under low paired rates. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed method consistently improves clustering performance under low paired rates compared with widely used IMC baselines.