  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.
