An exact approach to sparse principal component analysis
type: Item
instance of: scholarly article
title: An exact approach to sparse principal component analysis
zbMATH Open document ID: 1234.62093
author: Alessio Farcomeni
published in: Computational Statistics
publication date: 2011-09-08T00:00:00Z
review text: In sparse principal components analysis (sPCA) one looks for principal directions \(\beta\) in the set of vectors with a limited number of nonzero entries. E.g., the first sPCA component of the covariance matrix \(Z\) is defined as the solution of the optimization problem \(\max_\beta \beta' Z\beta\) under the constraints \(\beta'\beta=1\) and \(| \beta| _0\leq k_1\), where \(| \beta| _0\) is the number of nonzero entries in \(\beta\), and \(k_1\) is a fixed number (the degree of sparsity). The author proposes a new branch-and-bound algorithm for the exact solution of this problem and describes its application to the calculation of many (orthogonal or uncorrelated) sPCA components. The choice of the degree of sparsity is discussed. Results of simulations and real data analyses are presented.
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62-08
zbMATH DE Number: 5946106
zbMATH Keywords: branch and bound algorithm
zbMATH Keywords: degree of sparsity
describes a project that uses: DSPCA
describes a project that uses: R
MaRDI profile type: Publication
full work available at URL: s00180-008-0147-3
OpenAlex ID: W2085359512
Wikidata QID: Q59397202
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DOI: 10.1007/S00180-008-0147-3
description: scientific article; zbMATH DE number 5946106