Multi-Kernel Tensor Fusion on Grassmann Manifold for Genomic Data Clustering

Due to the inherent high-dimensional characteristics of genomic data, traditional single metric/kernel-based clustering methods fail to accurately perform data analysis. To address this issue, we propose a multi-kernel clustering with tensor fusion on the Grassmann manifold (MKCTM). Specifically, multiple kernel functions are employed to map data into different kernel spaces and utilize tensor representations to capture their high-order relationships. By introducing a tensor low-rank constraint, we maximize the correlation among kernels while separating the noise and redundancy information from kernel tensor. Finally, the learned kernel tensor is fused on the Grassmann manifold to obtain the final kernel matrix for enhancing clustering. We integrate tensor learning and tensor fusion steps into a unified optimization model and propose an efficient iterative optimization algorithm to solve it. Our proposed method is evaluated on six high-dimensional gene expression datasets against eight popular baseline methods. The remarkable experimental performance demonstrates the exceptional effectiveness of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git