| 引用本文: | 杨剑哲,孙巧榆,王君,程丹松,金野,石大明.基于改进增广拉格朗日乘子法的鲁棒性主成分分析[J].哈尔滨工业大学学报,2015,47(11):27.DOI:10.11918/j.issn.0367-6234.2015.11.005 |
| YANG Jianzhe,SUN Qiaoyu,WANG Jun,CHENG Dansong,JIN Ye,SHI Daming.Robust principal component analysis based on advanced augmented lagrange multiplier method[J].Journal of Harbin Institute of Technology,2015,47(11):27.DOI:10.11918/j.issn.0367-6234.2015.11.005 |
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| 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． |
| 关键词: 鲁棒性主成分分析 拉格朗日乘子的最优初始化 增广的拉格朗日乘子法 凸优化 高斯噪声 |
| DOI：10.11918/j.issn.0367-6234.2015.11.005 |
| 分类号:TP391 |
| 基金项目:国家自然科学基金科学(5,3)；国家博士后科学基金(20100480998);哈尔滨市科技创新人才专项资金 (2013RFQXJ110). |
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| Robust principal component analysis based on advanced augmented lagrange multiplier method |
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YANG Jianzhe1, SUN Qiaoyu2, WANG Jun1, CHENG Dansong1, JIN Ye1, SHI Daming1
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(1. School of Computer Science and Technology, Harbin Institute of Technology, 150001 Harbin, China; 2. School of Electronic Engineering, Huaihai Institute of Technology, 222005 Lianyungang, Jiangsu, China)
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| 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. |
| Key words: robust principal component analysis, optimal initialization of Lagrange multiplier, augmented Lagrange multiplier method, novel convex optimization model, Gaussian component |
