期刊名称:CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度:2008
卷号:1
出版社:Center for Operations Research and Econometrics (UCL), Louvain
摘要:In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose
two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a
single sparse dominant principal component of a data matrix, or more components at once, respectively.
While the initial formulations involve nonconvex functions, and are therefore computationally intractable,
we rewrite them into the form of an optimization program involving maximization of a convex function on
a compact set. The dimension of the search space is decreased enormously if the data matrix has many more
columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It
appears that our algorithm has best convergence properties in the case when either the objective function or
the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced
in the block case. Finally, we demonstrate numerically on a set of random and gene expression test
problems that our approach outperforms existing algorithms both in quality of the obtained solution and in
computational speed.