Abstract: Clustering is an important research content in the field of data mining and machine learning. Generally, similarity graphs are constructed based on data samples, and then the samples are divided into corresponding classes based on the similarity graphs. However, the real data is often damaged, resulting in inaccurate similarity graphs, which directly affects the clustering results. In order to solve these problems, a robust clustering-oriented adaptive graph adjustment and low-rank matrix decomposition method is proposed. The core idea of the method is to decompose the original data X into pure data D and noisy data S, then construct a Laplacian matrix based on pure data and perform adaptive graph adjustment. Subsequently, a joint learning framework is given, which integrates data separation, adaptive graph regularization, noise removal and low-rank matrix decomposition into an objective function. Use augmented Lagrangian multiplier method to update variables separately. Finally, the paper theoretically proves the convergence of the algorithm and conduct experiments. The experimental results show that the proposed method has certain advantages compared with some existing methods.

Key words: robust clustering, L_2,1 norm, low-rank matrix decomposition, adaptive graph regularization, augmented Lagrange multiplier method