Incomplete Multi-Omics Cancer Subtyping Via HSIC-regularized Exponential Tensor Learning and ℓ2,log Noise Modeling

Cancer subtype classification plays a crucial role in precision medicine and individualized therapy. With the continuous advancement of multi-omics profiling technologies, multi-view clustering has emerged as an effective framework for cancer subtype identification. However, practical multi-omics data are frequently challenged by missing views, noise in high-dimensional settings, and complex redundancy across views. In the context of these problems, we propose a tensorized incomplete multi-view subspace clustering framework for cancer subtyping. Specifically, the Hilbert–Schmidt Independence Criterion (HSIC) captures potential nonlinear statistical dependence among representation matrices from different views in a reproducing kernel Hilbert space, thereby strengthening cross-view consistency and complementary information exchange. In addition, the latent shared high-order low-rank structure in multi-view observations can be effectively characterized by an exponential nonconvex tensor nuclear norm. Meanwhile, an ℓ2,log-based group-sparse regularization term is employed to flexibly and robustly model structured outliers and noise. The resulting optimization problem is solved by an ADMM-based procedure equipped with iterative reweighting. Results obtained from several cancer multi-omics cohorts indicate that the proposed method achieves strong effectiveness and robustness in incomplete multi-view cancer subtyping.