Sparse PCA: Convex Relaxations, Algorithms and Applications - Mathematics > Optimization and ControlReport as inadecuate




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



Author: Youwei Zhang, Alexandre d'Aspremont, Laurent El Ghaoui

Source: https://arxiv.org/







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