一种新的基于非凸秩近似的RPCA模型

在机器学习、数据挖掘和图像处理等研究领域,鲁棒主成分分析(RPCA)主要用于恢复一个低秩的数据矩阵。考虑到核范数作为矩阵秩函数的凸近似在处理实际数据集时存在的问题,以及矩阵秩函数的非凸近似所展现出的优势,本文提出了一种新的非凸近似函数。基于该非凸近似函数,提出一个改进的RPCA模型,并应用增广拉格朗日乘子法对其进行求解。最后利用视频背景分离的实际数据,通过数值实验验证了新模型的有效性。

A New Nonconvex Rank Approximation of RPCA

Robust principal component analysis(RPCA) aimed to recover a low rank matrix in applications of data mining, machine learning and image processing. The nuclear norm exists some disadvantages when dealing with in real-world sets as a convex approximation of the matrix rank function. In this paper, a new non-convex approximation function is proposed, combining with the advantages of the non-convex approximation of rank function. An improved RPCA model is proposed based on the new non-convex approximation function, and the augmented Lagrange multiplier method is used to solve he improved model. Moreover, the numerical experiments with real-world application of video background separation show that our algorithms are helpful.