for Sparse Principal Component Analysis
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Optimal solutions for Sparse Principal Component Analysis Alexandre d'Aspremont, Francis Bach & Laurent El Ghaoui, Princeton University, INRIA/ENS Ulm & U.C. Berkeley Preprint available on arXiv 1
Voir
- g1 g2
- pca sparse
- also hard
- genes
- alexandre d'aspremont
- get sparse factors
- numerically cheap
Optimal solutions
for Sparse Principal Component Analysis
Alexandre d’Aspremont, Francis Bach & Laurent El Ghaoui,
Princeton University, INRIA/ENS Ulm & U.C. Berkeley
Preprint available on arXiv
1
Principal Component Analysis
Introduction
•Classic dimensionality reduction tool. •Numerically cheap:O(n2)as it only requires computing a few dominant eigenvectors.
Sparse PCA
•Getsparsefactors capturing a maximum of variance. • problem. combinatorialNumerically hard: •Controlling the sparsity of the solution is also hard in practice.
2
10
5
0
−5 −5
0
PCA
Inrtod
−5 0 5 510 f210 15f1
uciton
3 2 1 0 −1 1 0 −1
Sparse PCA
0 1 −2 2 −33g2 g1−4
−1
Clustering of the gene expression data in the PCA versus sparse PCA basis with 500 genes. The factorsfon the left are dense and each use all 500 genes while the sparse factorsg1 g2andg3on the right involve 6, 4 and 4 genes respectively. (Data: Iconix Pharmaceuticals)
3
