计算机科学 ›› 2017, Vol. 44 ›› Issue (1): 243-246.doi: 10.11896/j.issn.1002-137X.2017.01.045
谭亚芳,刘娟,王才华,蒋万伟
TAN Ya-fang, LIU Juan, WANG Cai-hua and JIANG Wan-wei
摘要： 主成分分析(Principal Component Analysis,PCA)是一种用线性变换选出少数重要变量(降维)的多元统计分析方法。虽然传统PCA被广泛应用于科学研究与工程领域中,但是其结果有时很难解释。因此,一些研究人员引入稀疏约束项(lasso、fused lasso以及adaptive lasso等),以得到可解释的结果。由于传统稀疏项的稀疏度不容易控制,为此引入一种新的约束项,即稀疏可控惩罚项(Sparse Controllable penalty,SCP),来控制主成分的稀疏程度。与传统的约束项相比,SCP具有长度不敏感、维度不敏感和约束项的取值范围在0到1之间的优点。这些优点极大地降低了调节稀疏度的难度。实验表明,稀疏可控主成分分析(Sparse Controllable Principal component Analysis,SCPCA)是高效的。
| [1] JOLLIFFE I T.Principal Component Analysis(second ed.)[M].New York,Springer,2002. [2] HASTIE T,TIBSHIRANI R,FRIEDMAN J.The Elements of Statistical Learning [M].Data mining,Interface and Prediction New York,Springer,2001. [3] HANCOCK P J B,BURTON A M,BRUCE V.Face processing:human perception and principal components analysis [J].Memory and Cognition,1996,24(1):26-40. [4] MISRA J,SCHMITT W,et al.Interactive Exploration of Microarray Gene Expression Patterns in a Reduced Dimensional Space [J].Genome Research,2012,12(7):1112-1120. [5] SHEN Hai-peng,HUANG Jian-hua.Sparse principal component analysis via regularized low rank matrix approximation [J].Journal of Multivariate Analysis,2008,99(6):1015-1034. [6] JOLLIFFE I T,UDDIN M.The Simplified Component Tech-nique:An Alternative to Rotated Principal Components[J].Journal of Computational and Graphical Statistics,2000,9(9):689-710. [7] JOLLIFFE I T,TRENDAFILOV N T,et al.A Modified Principal Component Technique Based on the LASSO [J].Journal of Computational and Graphical Statistics,2003,12(3):531-547. [8] ZOU H,HASTIE T,et al.Sparse principal component analysis [J].Journal of Computational and Graphical Statistics,2006,15:265-286. [9] WITTEN D M,et al.A penalized matrix decomposition,withapplications to sparse principal components and canonical correlation [J].Biostatistics,2009,10(3):515-534. [10] TIBSHIRANI R.Regression shrinkage and selection via the lasso [J].Journal of the Royal Statistical Society,1996,58(1):267-288. [11] ZOU H.The adaptive lasso and its oracle properties [J].Journal of the American Statistical Association,2006,101(476):1418-1429. [12] ALLEN G I,GROSENICK L,et al.the A Generalized Least-Square Matrix Decomposition [J].Journal of the American Statistical Association,2014,109(505):145-159. [13] QI Xin,LUO Rui-yan,ZHAO Hong-yu.Sparse principal component analysis by choice of norm[J].Journal of Multivariate Analysis,2013,114(2):127-160. |
| No related articles found! |
|
||
首页