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For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method \cite{JZ} to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in \cite{WYLZ}. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.
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참고문헌 (27)
참고문헌 신청
Z. Allen-Zhu / 2016 / Variance Reduction for Faster Non-Convex Optimization
Z. Allen-Zhu / 2017 / LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain
Z. Allen-Zhu / 2016 / Improved SVRG for Non-Strongly-Convex or Sum-of-NonConvex Objectives
J. Barzilai / 1988 / Two-point step size gradient methods / IMA J. Numer. Anal. 8(1):141~148
L. Bottou / 2016 / Optimization Methods for Large-Scale Machine Learning
Z. Allen-Zhu / 2017 / LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain
Z. Allen-Zhu / 2016 / Improved SVRG for Non-Strongly-Convex or Sum-of-NonConvex Objectives
J. Barzilai / 1988 / Two-point step size gradient methods / IMA J. Numer. Anal. 8(1):141~148
L. Bottou / 2016 / Optimization Methods for Large-Scale Machine Learning
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