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ICML
2007
IEEE

Full regularization path for sparse principal component analysis

9 years 12 months ago
Full regularization path for sparse principal component analysis
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a particular 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. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all numbers of non zero coefficients, with complexity O(n3 ), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n3 ). We show on toy examples and biological data that our algorithm does provide globally optimal solutions in many cases.
Alexandre d'Aspremont, Francis R. Bach, Laurent El
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Alexandre d'Aspremont, Francis R. Bach, Laurent El Ghaoui
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