Graph regularized low-rank representation for submodule clustering

Abstract

In this paper, a new submodule clustering method for imaging (2-D) data is proposed. Unlike most existing clustering methods that first convert such data into vectors as preprocessing, the proposed method arranges the data samples as lateral slices of a third-order tensor. Our algorithm is based on the union-of-free-submodules model and the samples are represented using t-product in the third-order tensor space. First, we impose a low-rank constraint on the representation tensor to capture the principle information of data. By incorporating manifold regularization into the tensor factorization, the proposed method explicitly exploits the local manifold structure of data. Meanwhile, a segmentation dependent term is employed to integrate the two pipeline steps of affinity learning and spectral clustering into a unified optimization framework. The proposed method can be efficiently solved based on the alternating direction method of multipliers and spectral clustering. Finally, a nonlinear extension is proposed to handle data drawn from a mixture of nonlinear manifolds. Extensive experimental results on five real-world image datasets confirm the effectiveness of the proposed methods.