Robust subspace clustering based on non-convex low-rank approximation and adaptive kernel

Abstract As a relatively advanced method, the low-rank kernel space clustering method shows good performance in dealing with nonlinear structure of high-dimensional data. Unfortunately, this method is sensitive to large corruptions and doesn’t balance the contribution of all singular values. To solve the above problems, the low-rank kernel method is modified, and a robust subspace clustering method (LAKRSC) based on non-convex low-rank approximation and adaptive kernel is proposed. In our model, the weighted Schatten p-norm is introduced to balance the importance of different singular values, which can more accurately approximate the rank function and be more flexible in practical applications. Therefore, applying weighted Schatten p-norm to adaptive kernel can approximate the original low rank hypothesis better when the data is mapped into the feature space. In addition, our model uses correntropy to handle complex noise which enhances the robustness of the model. A new algorithm HQ&ADMM, combined by Half-Quadratic technique (HQ) and ADMM, is studied to solve our model. Experiments on four real-world datasets show that the clustering performance of LAKRSC is significantly better than that of several more advanced methods.