Auto-weighted multiple kernel tensor clustering

Multiple kernel subspace clustering (MKSC) has attracted intensive attention since its powerful capability of exploring consensus information by generating a high-quality affinity graph from multiple base kernels. However, the existing MKSC methods still exist the following limitations: (1) they essentially neglect the high-order correlations hidden in different base kernels; and (2) they perform candidate affinity graph learning and consensus affinity graph learning in two separate steps, where suboptimal solution may be obtained. To alleviate these problems, a novel MKSC method, namely auto-weighted multiple kernel tensor clustering (AMKTC), is proposed. Specifically, AMKTC first integrates the consensus affinity graph learning and candidate affinity graph learning into a unified framework, where the optimal goal can be achieved by making these two learning processes negotiate with each other. Further, an auto-weighted fusion scheme with one-step manner is proposed to learn the final consensus affinity graph, where the reasonable weights will be automatically learned for each candidate graph. Finally, the essential high-order correlations between multiple base kernels can be captured by leveraging tensor-singular value decomposition (t-SVD)-based tensor nuclear norm constraint on a 3-order graph tensor. Experiments on seven benchmark datasets with eleven comparison methods demonstrate that our method achieves state-of-the-art clustering performance.