Multi-kernel clustering with tensor fusion on Grassmann manifold for high-dimensional genomic data.

The high dimensionality and noise challenges in genomic data make it difficult for traditional clustering methods. Existing multi-kernel clustering methods aim to improve the quality of the affinity matrix by learning a set of base kernels, thereby enhancing clustering performance. However, directly learning from the original base kernels presents challenges in handling errors and redundancies when dealing with high-dimensional data, and there is still a lack of feasible multi-kernel fusion strategies. To address these issues, we propose a Multi-Kernel Clustering method with Tensor fusion on Grassmann manifolds, called MKCTM. Specifically, we maximize the clustering consensus among base kernels by imposing tensor low-rank constraints to eliminate noise and redundancy. Unlike traditional kernel fusion approaches, our method fuses learned base kernels on the Grassmann manifold, resulting in a final consensus matrix for clustering. We integrate tensor learning and fusion processes into a unified optimization model and propose an effective iterative optimization algorithm for solving it. Experimental results on ten datasets, comparing against 12 popular baseline clustering methods, confirm the superiority of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git.