Sparse PCA: Convex Relaxations, Algorithms and Applications

Youwei Zhang (), Alexandre d’Aspremont () and Laurent El Ghaoui ()
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Youwei Zhang: EECS, University of California
Alexandre d’Aspremont: ORFE, Princeton University
Laurent El Ghaoui: EECS, University of California

Chapter Chapter 31 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 915-940 from Springer

Abstract: Abstract Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. Unfortunately, this problem is also combinatorially hard and we discuss convex relaxation techniques that efficiently produce good approximate solutions. We then describe several algorithms solving these relaxations as well as greedy algorithms that iteratively improve the solution quality. Finally, we illustrate sparse PCA in several applications, ranging from senate voting and finance to news data.

Keywords: Principal Component Analysis; Greedy Algorithm; Semidefinite Program; Sample Covariance Matrix; Semidefinite Relaxation (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_31

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