基于改进增广拉格朗日乘子法的鲁棒性主成分分析

Robust principal component analysis based on advanced augmented lagrange multiplier method

摘要:

针对增广的拉格朗日乘子法在求解鲁棒性主成分分析,特别是当数据同时受到稀疏噪声和高斯噪声的干扰时,计算精度会降低,数据降维去噪任务不能很好完成的情况,提出改进的增广拉格朗日乘子法来解决上述问题．一是用基于最优乘子初始化的改进增广拉格朗日乘子法来提高算法的计算精度,二是针对鲁棒性主成分分析,提出一个带高斯噪声的凸优化模型．实验结果表明,本文提出的最优乘子初始化改进算法赋予增广的拉格朗日乘子法一个最优的拉格朗日乘子,从而提高算法的计算精度,而凸优化模型能够清晰地将高斯噪声和稀疏噪声从数据矩阵中分离出去,进而提高数据对高斯噪声的鲁棒性．

Abstract:

To solve the problem that the calculation accuracy of the robust principal component analysis is reduced when the high dimensional data is disturbed by the sparse large noise and Gaussian noise at the same time, this paper proposes the advanced augmented Lagrange multiplier method for the robust principal component analysis. On one hand, we enhance the calculation accuracy by the advanced method which is based on the optimal initialization of the Lagrange multiplier. On the other hand we propose a dual noise convex optimization model for the robust principal component analysis. As the experimental results shown, the proposed advanced method provides an optimal multiplier for the augmented Lagrange multiplier method and enhances the calculation accuracy of the method. Besides, the proposed dual noise model can separate the Gaussian noise and sparse noise from the data clearly and reinforces the robustness of the robust principal component analysis facing with dual noise.