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Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable distant-distance similarity estimation would degrade clustering per-formance. Although existing localized MKC algorithms exhibit improved performance compared to globally-designed competi-tors, most of them widely adopt KNN mechanism to localize kernel matrix by accounting for τ -nearest neighbors. However, such a coarse manner follows an unreasonable strategy that the ranking importance of different neighbors is equal, which is impractical in applications. To alleviate such problems, this paper proposes a novel local sample-weighted multiple kernel clustering (LSWMKC) model. We first construct a consensus discriminative affinity graph in kernel space, revealing the latent local structures. Further, an optimal neighborhood kernel for the learned affinity graph is output with naturally sparse property and clear block diagonal structure. Moreover, LSWMKC im-plicitly optimizes adaptive weights on different neighbors with corresponding samples. Experimental results demonstrate that our LSWMKC possesses better local manifold representation and outperforms existing kernel or graph-based clustering algo-rithms. The source code of LSWMKC can be publicly accessed from https://github.com/liliangnudt/LSWMKC.