for Sparse Principal Component Analysis

Francis Bach

Description

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

• g1 g2


• pca sparse


• also hard


• genes


• alexandre d'aspremont


• get sparse factors


• numerically cheap

Sujets

• Princeton University

Informations

• Publié par: pefav
• Nombre de lectures: 17
• Langue: English

Extrait

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(n 2 )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 5 10 f 2 10 15 f 1

uciton

3 2 1 0 −1 1 0 −1

Sparse PCA

0 1 −2 2 −3 3 g 2 g 1 −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 factorsg 1  g 2 andg 3 on the right involve 6, 4 and 4 genes respectively. (Data: Iconix Pharmaceuticals)

3