Principal Component Analysis by Optimization of Symmetric Functions has no Spurious Local Optima

DOI10.1137/18M1188495zbMath1430.90468arXiv1805.07459OpenAlexW3005010158MaRDI QIDQ5215520

Armin Eftekhari, Raphael Hauser

Publication date: 12 February 2020

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.07459

zbMATH Keywords

principal component analysisnonconvex optimizationsaddle point property

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Factorization of matrices (15A23) Nonconvex programming, global optimization (90C26) Eigenvalues, singular values, and eigenvectors (15A18)

Uses Software

• SDPLR
• ElemStatLearn

Cites Work

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• Generalized power method for sparse principal component analysis
• The Geometry of Algorithms with Orthogonality Constraints
• Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks
• Streaming Principal Component Analysis From Incomplete Data
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• RELATIONS BETWEEN TWO SETS OF VARIATES
• Quadratic expansions of spectral functions

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