Kernel Truncated Regression Representation for Robust Subspace Clustering

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering methods assume that the data could be linearly represented with each other in the input space. In practice, however, this assumption is hard to be satisfied. To achieve nonlinear subspace clustering, we propose a novel method which consists of the following three steps: 1) projecting the data into a hidden space in which the data can be linearly reconstructed from each other; 2) calculating the globally linear reconstruction coefficients in the kernel space; 3) truncating the trivial coefficients to achieve robustness and block-diagonality, and then achieving clustering by solving a graph Laplacian problem. Our method has the advantages of a closed-form solution and capacity of clustering data points that lie in nonlinear subspaces. The first advantage makes our method efficient in handling large-scale data sets, and the second one enables the proposed method to address the nonlinear subspace clustering challenge. Extensive experiments on five real-world datasets demonstrate the effectiveness and the efficiency of the proposed method in comparison with ten state-of-the-art approaches regarding four evaluation metrics.