In multi-view clustering, different views may have different confidence levels when learning a consensus representation. Existing methods usually address this by assigning distinctive weights to different views. However, due to noisy nature of real-world applications, the confidence levels of samples in the same view may also vary. Thus considering a unified weight for a view may lead to suboptimal solutions. In this paper, we propose a novel localized multi-view subspace clustering model that considers the confidence levels of both views and samples. By assigning weight to each sample under each view properly, we can obtain a robust consensus representation via fusing the noiseless structures among views and samples. We further develop a regularizer on weight parameters based on the convex conjugacy theory, and samples weights are determined in an adaptive manner. An efficient iterative algorithm is developed with a convergence guarantee. Experimental results on four benchmarks demonstrate the correctness and effectiveness of the proposed model.
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