一种基于低秩表示的子空间聚类改进算法

Improved Algorithm Based on Low Rank Representation for Subspace Clustering

该文针对现有的基于低秩表示的子空间聚类算法使用核范数来代替秩函数,不能有效地估计矩阵的秩和对高斯噪声敏感的缺陷,提出一种改进的算法,旨在提高算法准确率的同时,保持其在高斯噪声下的稳定性。在构建目标函数时,使用系数矩阵的核范数和Forbenius范数作为正则项,对系数矩阵的奇异值进行强凸的正则化后,采用非精确的增广拉格朗日乘子方法求解,最后对求得的系数矩阵进行后处理得到亲和矩阵,并采用经典的谱聚类方法进行聚类。在人工数据集、Extended Yale B数据库和PIE数据库上同流行的子空间聚类算法的实验对比证明了所提改进算法的有效性和对高斯噪声的鲁棒性。

The nuclear norm is used to replace the rank function in the subspace clustering algorithm based on low rank representation, it can not estimate the rank of the matrix effectively and it is sensitive to Gauss noise. In this paper, a novel algorithm is proposed to improve the accuracy and maintain its stability under the Gauss noise. When building the objective function, the nuclear norm and Forbenius norm of coefficient matrix are used as the regularization terms, after a strong convex regularizer over singular values of coefficient matrix, an inexact augmented Lagrange multiplier method is utilized to solve the problem. Finally, the affinity matrix is acquired by post-processing of coefficient matrix and the classical spectral clustering method is employed to clustering. The experimental comparison results between the state-of-the-art algorithms on synthetic data, Extended Yale B and PIE datasets demonstrate the effectiveness of the proposed improved method and the robustness to Gauss noise.