Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this assumption usually does not hold. To achieve nonlinear subspace clustering, we propose a novel method, called kernel truncated regression representation. Our method consists of the following four steps: 1) projecting the input data into a hidden space, where each data point can be linearly represented by other data points; 2) calculating the linear representation coefficients of the data representations in the hidden space; 3) truncating the trivial coefficients to achieve robustness and block-diagonality; and 4) executing the graph cutting operation on the coefficient matrix by solving a graph Laplacian problem. Our method has the advantages of a closed-form solution and the capacity of clustering data points that lie on nonlinear subspaces. The first advantage makes our method efficient in handling large-scale datasets, and the second one enables the proposed method to conquer the nonlinear subspace clustering challenge. Extensive experiments on six benchmarks demonstrate the effectiveness and the efficiency of the proposed method in comparison with current state-of-the-art approaches. © 2020 Elsevier Inc.
Bibliographical noteThis work was supported by the National Natural Science Foundation of China under grants 61432012 , 61329302 , 61625204 , 61971296 and U19A2078 , the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under grant EP/J017515/1, the Ministry of Education & China Mobile Research Funding (Grant No. MCM20180405), the Sichuan Science and Technology Planning Projects (Grants No. 2019YFG0495 and 2019YFH0075), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No. 2017ZT07X386), Shenzhen Peacock Plan (Grant No. KQTD2016112514355531), the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284) and the Program for University Key Laboratory of Guangdong Province (Grant No. 2017KSYS008).
- Kernel techniques
- Kernel truncated regression
- Nonlinear subspace clustering
- Spectral clustering