Robust clustering with sparse corruption via [formula omitted], [formula omitted] norm constraint and Laplacian regularization

Abstract

Clustering has been applied in machine learning, data mining and so on, and has received extensive attention. However, since some data has noise or outliers, these noise or outliers easily bring about the objective function with large errors. In this paper, a robust clustering model with ℓ2,1, ℓ1 norm and Laplacian regularization (RCLR) is proposed, on which, sparse error matrix is introduced to express sparse noise, and ℓ1 norm is introduced to alleviate the sparse noise. In addition, the ℓ2,1 norm is also introduced to achieves space robust by virtue of its nice rotation invariance property. Therefore, our RCLR is insensitive to data noise and outliers. More importantly, the Laplacian regularization is introduced into the RCLR to improve the clustering accuracy. In order to solve the optimization objective of clustering problem, we propose an iterative updating algorithm, named alternating direction method of multipliers (ADMM), to update each optimization variable alternatively, and the convergence of the proposed algorithm is also proved in theory. Finally, experimental results on a total of eleven datasets of three types of datasets, elaborate the superiority of this method over six existing classical clustering methods. Three types of datasets include face images dataset, handwritten recognition dataset, and UCI dataset. In particular, our RCLR clustering approach has the best effect on face image dataset.