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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 (<jats:italic>t<\/jats:italic>-SVD)-based tensor nuclear norm constraint on a 3-order graph tensor. 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