An exact approach to sparse principal component analysis

被引:0
作者
Alessio Farcomeni
机构
[1] Università di Roma “La Sapienza”,
来源
Computational Statistics | 2009年 / 24卷
关键词
Branch and bound; Dimension reduction; Feature selection; Feature extraction; Interleaving eigenvalues theorem; Sparse principal components;
D O I
暂无
中图分类号
学科分类号
摘要
We show a branch and bound approach to exactly find the best sparse dimension reduction of a matrix. We can choose between enforcing orthogonality of the coefficients and uncorrelation of the components, and can explicitly set the degree of sparsity. We suggest methods to choose the number of non-zero loadings for each component; illustrate and compare our approach with existing methods through a benchmark data set.
引用
收藏
页码:583 / 604
页数:21
相关论文
共 30 条
[1]  
Cadima J(1995)Loadings and correlations in the interpretation of principal components J Appl Stat 22 203-214
[2]  
Jolliffe IT(1994)On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds Math Program 67 189-224
[3]  
Coleman TF(2004)Detecting collaborations in text comparing the authors’ rhetorical language choices in The Federalist Papers Comput Hum 38 15-36
[4]  
Li Y(2007)A direct formulation for sparse PCA using semidefinite programming SIAM Rev 49 434-448
[5]  
Collins J(2003)An introduction to variable and feature selection J Mach Learn Res 3 1157-1182
[6]  
Jaufer D(1978)Hedonic prices and the demand for clean air J Environ Econom Manage 5 81-102
[7]  
Vlachos P(1965)A rationale and test for the number of factors in factor analysis Psychometrika 30 179-185
[8]  
Butler B(1967)Two case studies in the application of principal components Appl Stat 16 225-236
[9]  
Suguru I(1995)Rotation of principal components: choice of normalization constraints J Appl Stat 22 29-35
[10]  
d’Aspremont A(2003)A modified principal component technique based on the lasso J Comput Graph Stat 12 531-547