稀疏主成分分析的两阶段法
Two-Stage Method of Sparse Principal Component Analysis
摘要: 本文提出稀疏主成分分析的两阶段法，即先求解主成分，然后添加l1正则化项得到稀疏载荷，并利用坐标下降法求解模型。方法简单易操作。另外，本文还提出了一种可以确定两阶段模型中惩罚参数的算法，通过选取合适的惩罚参数，可以使稀疏主成分方差和主成分相关性等性能指标取得折衷。
Abstract: In this paper, we propose a sparse principal component based on two-stage method, that is, we first get principal component, and then add the l1 regular term of the loadings. Coordinate descent method is used to solve the model. The model is easy to understand. In addition, this paper proposes a heuristic algorithm which can determine the penalty parameters in the model. By se-lecting the appropriate penalty parameters, the sparse principal component explained variance and sparsity can be optimized at the same time.
文章引用：杨欣. 稀疏主成分分析的两阶段法[J]. 应用数学进展, 2017, 6(9): 1174-1181. https://doi.org/10.12677/AAM.2017.69142

参考文献

[1] Cadima, J. and Jollife, I.T. (1995) Loading and Correlations in the Interpretation of Principal Components. Journal of Applied Statistics, 22, 203-214.
[Google Scholar] [CrossRef] 
[2] Hausman, R. (1982) Constrainted Mul-tivariate Analysis in Optimization in Statistics. North Holland, Amsterdam, 137-151.
[3] Jolliffe, I.T., Trendafilov, N.T. and Uddin, M. (2003) A Modified Principal Component Technique Based on the LASSO. Journal of Computational and Graphical Statistics, 12, 531-547.
[Google Scholar] [CrossRef] 
[4] Tibshirani, R. (1996) Regression Shrinkage and Selection via Lasso. Journal of the Royal Statistical Society, Series B (Methodological), 58, 267-268.
[5] Hastie, T., Tibshirani, R. and Wainwright, M. (2016) Statistical Learning with Sparsity. A Chapman & Hall Book.
[6] Hsieh, C.J., Chang, K.W., Lin, C.J., et al. (2008) A Dual Coordinate Descent Method for Large-Scale Linear SVM. Proceedings of the 25th International Conf on Machine Learning, ACM, New York, 408-415.
[7] Zou, H., Hastie, T. and Tibshirani, R. (2012) Sparse Principal Component Analysis. Journal of Computational and Graphical Statistics, 15, 265-286.
[Google Scholar] [CrossRef] 
[8] Lu, Z. and Zhang, Y. (2012) An Augmented Lagrangian Approach for Sparse Principal Component Analysis. Mathematical Programming, 135, 149-193.
[Google Scholar] [CrossRef] 
[9] Journee, M., Nesterov, Y. and Richtarik, P. (2010) Generalized Power Method for Sparse Principal Component Analysis. The Journal of Machine Learning Research, 11, 517-553.
[10] Jeffers, J.N.R. (1967) Two Case Studies in the Application of Principal component Analysis. Applied Statistics, 16, 225-236.
[Google Scholar] [CrossRef] 
[11] Alon, U., Barkai, N., Notterman, D.A., et al. (1999) Broad Patterns of Gene Expression Revealed by Clustering of Tumor and Normal Colon Tissues Probed by Oligonu-cleotide Arrays. Proceedings of the National Academy of Sciences of the United States of America, 96, 6745-6750.
[Google Scholar] [CrossRef] [PubMed]

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