Purity-Preserving Kernel Tensor Low-Rank Learning for Robust Subspace Clustering

In recent years, multi-kernel learning (MKL) methods have been widely used in performing nonlinear data subspace clustering tasks, benefiting from the fact that they do not require the selection and tuning of predefined kernels. However, the effect of raw noise on the data structure in the feature space has been neglected in most MKL studies so far. In this paper, we propose a robust subspace clustering method called purity kernel tensor low-rank learning (KTLL), which effectively isolates noise transfer from the original data space to the high-dimensional feature space. Specifically, we construct the kernel pool obtained by MKL as a primitive third-order kernel tensor, separate the corrupted information in the feature space, and use the separated pure kernel tensor to learn the optimal affinity matrix. The tensor learning of the kernel pool can effectively mine the higher-order correlations among different kernel matrices, thus improving the clustering performance of KTLL.We have conducted extensive experiments to compare KTLL with state-of-the-art MKL and deep subspace clustering algorithms, and our results demonstrate the superiority of KTLL.