One-step subspace clustering based on adaptive graph regularization and correntropy induced metric

Subspace clustering is very significant and widely used in computer vision and pattern recognition. Traditional self-expressive subspace clustering methods usually separate similarity measurement and data clustering into two steps, so they fail to fully consider the interdependence between them. Moreover, since some graph parameters need to be defined in advance, it is difficult to select the optimal graph parameters, which leads to the loss of local smoothness. Furthermore, classic methods are optimal for independent and identically distributed gaussian noise but sensitive to outliers. To solve the above problems effectively, one-step subspace clustering based on adaptive graph regularization and correntropy induced metric (OSCA) is proposed in this paper. Specifically, OSCA applies subspace structured norm to measure the uncertainty of two steps of similarity measurement and data clustering, integrating these two independent steps into a unified framework. Meanwhile, according to the local connectivity of data, an adaptive optimal neighborhood is assigned to each data point to learn the coefficient matrix, so that the global structure and local structure of data can be considered. In addition, the correntropy, which is insensitive to outliers, is cleverly exploited to calculate the reconstruction error to handle complex noise better. Finally, the HQ-ADMM algorithm (an efficient interactive algorithm) is proposed to optimize the model. Experimental results on ten datasets of four types show that the proposed method can significantly improve the clustering performance.