鲁棒主成分分析模型综述
A Review of Robust Principal Component Analysis Models
摘要:
主成分分析求解的模型适用于去除密集的高斯小噪声，但是对于非高斯噪声或离群点严重的噪声时，主成分分析法去噪效果很不理想，缺乏鲁棒性。针对主成分分析模型的缺点提出了鲁棒主成分分析模型。本文在鲁棒主成分分析的相关理论基础下，研究了鲁棒主成分分析的几种经典模型的去噪效果。通过实验数据及图片的效果，分析对比这几个模型的优缺点。
Abstract:
The model solved by principal component analysis is suitable for removing dense Gaussian small noise, but for non-gaussian noise or noise with serious outliers, the denoising effect of principal component analysis is not ideal and lacks robustness. A robust principal component analysis model was proposed to overcome the shortcomings of the PCA model. Based on the theory of robust principal component analysis, this paper studies the denoising effects of several classical models of RPCA. The advantages and disadvantages of these models are analyzed and compared through the results of experimental data and pictures.
参考文献
|
[1]
|
史加荣, 郑秀云, 魏宗田, 等. 低秩矩阵恢复算法综述[J]. 计算机应用研究, 2013, 30(6): 1601-1605.
|
|
[2]
|
肖萌. 改进的鲁棒主成分分析模型及其应用[D]: [硕士学位论文]. 重庆: 重庆大学, 2016.
|
|
[3]
|
Papamakarios, G. (2014) Robust Low-Rank Modelling on Matrices and Tensors. MSc Thesis, Department of Computing, Imperial College, London.
|
|
[4]
|
Cabral, R., Torre, F.D.L., Costeira, J.P., et al. (2013) Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition. Proceedings of the 2013 IEEE International Conference on Computer Vision, IEEE. [Google Scholar] [CrossRef]
|
|
[5]
|
Bao, B.K., Liu, G., Xu, C., et al. (2012) Inductive Robust Principal Component Analysis. IEEE Transactions on Image Processing, 21, 3794-3800. [Google Scholar] [CrossRef]
|
|
[6]
|
Liu, G. and Yan, S. (2012) Active Subspace: Toward Scalable Low-Rank Learning. Neural Computation, 24, 3371-3394. [Google Scholar] [CrossRef]
|