Sparse Principal Component Analysis
@article{Zou2006SparsePC, title={Sparse Principal Component Analysis}, author={Hui Zou and Trevor J. Hastie and Robert Tibshirani}, journal={Journal of Computational and Graphical Statistics}, year={2006}, volume={15}, pages={265 - 286} }
Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified principal components with sparse loadings. We first show that PCA can be formulated as a regression…
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References
SHOWING 1-10 OF 26 REFERENCES
A Modified Principal Component Technique Based on the LASSO
- Mathematics
- 2003
In many multivariate statistical techniques, a set of linear functions of the original p variables is produced. One of the more difficult aspects of these techniques is the interpretation of the…
Simple principal components
- Mathematics, Computer Science
- 2000
An algorithm for producing simple approximate principal components directly from a variance–covariance matrix using a series of ‘simplicity preserving’ linear transformations that can always be represented by integers.
Principal Component Analysis
- Mathematics, Geology
- 2002
Introduction * Properties of Population Principal Components * Properties of Sample Principal Components * Interpreting Principal Components: Examples * Graphical Representation of Data Using…
Regression Shrinkage and Selection via the Elastic Net , with Applications to Microarrays
- Computer Science
- 2003
The elastic net is proposed, a new regression shrinkage and selection method that can be used to construct a classification rule and do automatic gene selection at the same time in microarray data, where the lasso is not very satisfied.
Regression Shrinkage and Selection via the Lasso
- Computer Science
- 1996
A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Regularization and variable selection via the elastic net
- Computer Science
- 2005
It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
Rotation of principal components: choice of normalization constraints
- Physics
- 1995
Following a principal component analysis, it is fairly common practice to rotate some of the components, often using orthogonal rotation. It is a frequent misconception that orthogonal rotation will…
A new approach to variable selection in least squares problems
- Mathematics, Computer Science
- 2000
A compact descent method for solving the constrained problem for a particular value of κ is formulated, and a homotopy method, in which the constraint bound κ becomes the Homotopy parameter, is developed to completely describe the possible selection regimes.
Interactive exploration of microarray gene expression patterns in a reduced dimensional space.
- BiologyGenome research
- 2002
In this study, PCA projection facilitated discriminatory gene selection for different tissues and identified tissue-specific gene expression signatures for liver, skeletal muscle, and brain samples.
Singular value decomposition for genome-wide expression data processing and modeling.
- BiologyProceedings of the National Academy of Sciences of the United States of America
- 2000
Using singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype.