Stochastic Gauss-Newton algorithms for online PCA

DOI10.1007/s10915-023-02289-0zbMath1520.65021arXiv2203.13081MaRDI QIDQ6111665

Liwei Xu, Xin Liu, Siyun Zhou

Publication date: 4 August 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13081

zbMATH Keywords

Gauss-Newton methodadaptive stepsizeonline principal component analysissymmetric low-rank product

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Probabilistic models, generic numerical methods in probability and statistics (65C20) Eigenvalues, singular values, and eigenvectors (15A18)

Cites Work

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• Near-optimal stochastic approximation for online principal component estimation
• Convergence analysis of Oja's iteration for solving online PCA with nonzero-mean samples
• Global convergence of Oja's PCA learning algorithm with a non-zero-approaching adaptive learning rate
• A simplified neuron model as a principal component analyzer
• A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
• Principal component analysis.
• Semigroups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
• Efficiency of minimizing compositions of convex functions and smooth maps
• Trace-penalty minimization for large-scale eigenspace computation
• Minimax sparse principal subspace estimation in high dimensions
• Simultaneous iteration method for symmetric matrices
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions
• Principal component analysis: a review and recent developments
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems
• GNMR: A Provable One-Line Algorithm for Low Rank Matrix Recovery
• Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints
• Accelerating Convergence by Augmented Rayleigh--Ritz Projections For Large-Scale Eigenpair Computation
• An Introduction to Matrix Concentration Inequalities
• An Efficient Gauss--Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations
• The method of stochastic approximation for the determination of the least eigenvalue of a symmetrical matrix
• A Stochastic Approximation Method
• Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?

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