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Impressive performance has been achieved when learning graphs from data in clustering tasks. However, real data often contain considerable noise, which leads to unreliable or inaccurate constructed graphs. In this paper, we propose adaptive data correction-based graph clustering (ADCGC), which can be used to adaptively remove errors and noise from raw data and improve the performance of clustering. The ADCGC method mainly contains three advantages. First, we design the weighted truncated Schatten p-norm (WTSpN) instead of the nuclear norm to recover the low-rank clean data. Second, we choose clean data samples that represent the essential properties of the data as the vertices of the undirected graph, rather than using all the data feature points. Third, we adopt the block-diagonal regularizer to define the edge weights of the graph, which helps to learn an ideal affinity matrix and improve the performance of clustering. In addition, an efficient iterative scheme based on the generalized soft-thresholding operator and alternating minimization is developed to directly solve the nonconvex optimization model. Experimental results show that ADCGC both quantitatively and visually outperforms existing advanced methods. [ABSTRACT FROM AUTHOR]

Multi-kernel subspace clustering has attracted widespread attention, because it can process nonlinear data effectively. It usually solves the representation coefficient between data by the subspace clustering optimization model, and then the constructed affinity matrix is input into the spectral clustering method to get the final clustering result. Obviously, the quality of the affinity matrix (graph) has a significant impact on the final clustering result. Unfortunately, there are two deficiencies in the previous multi-kernel subspace clustering methods as follows: 1) this typical two-phase method restricts the learning of the affinity matrix; 2) it does not fully extract the data global structure mapped to the kernel space. In order to solve these two problems simultaneously, a novel low-rank multi-kernel subspace clustering method incorporating a joint learning scheme, namely JALSC, is proposed. The innovation of this method is reflected in the following two aspects: 1) the adaptive local structure is used to learn the representation of the data and the affinity graph in the integrated objective function at the same time. The optimal affinity graph obtained by the one-step learning scheme helps to improve the clustering performance; 2) our method uses a non-convex low-rank approximation function to constrain the consensus kernel to preserve the global structure of the data after mapping to the feature space. A mass of experiments on several commonly used datasets show that JALSC obtains the best clustering performance and has better robustness compared with several advanced multi-kernel clustering methods. [ABSTRACT FROM AUTHOR]