Multi-kernel subspace stable clustering with exact rank constraints

The identification of cancer subtypes plays a critical role in the early diagnosis of cancer and the delivery of appropriate treatment. Clustering based on comprehensive multi-omic data often yields superior results than clustering using a single data type since each omic type may contain complementary information. However, existing clustering methods cannot fully explore the internal structural information within multiomic data and can lead to unstable clustering results. This paper proposes a novel multi-omic clustering framework, Multi -Kernel Subspace Stable Clustering with Exact Rank Constraints (MKSSC-ERC), which can effectively explore the correlation and complementary information between different omics types. Specifically, we design a kernel selection criterion that considers both accuracy and diversity and each omic data gets a base kernel. Then, we extract a consistent affinity matrix for these base kernels using subspace segmentation with exact rank constraints, which can refine the extracted shared structures and make them robust to sample noises. In addition, we devise a strategy for selecting the optimal initial cluster centers, which significantly enhances the stability of clustering results. Simulation studies on benchmark multi-omic datasets illustrate substantial gains over existing state-of-the-art methods in survival analysis. MKSSC-ERC is available at https://github.com/xuzihan66/MKSSC-ERC.