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We revisit the landscape of the simple matrix factorization problem.
Analysis of a complex of statistical variables into principal components
Harold Hotelling · 1933
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Relations between two sets of variates
Harold Hotelling · 1936
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Auto-association by multilayer perceptrons and singular value decomposition
Y. Bourlard, H.and Kamp · 1988
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Neural networks and principal component analysis: Learning from examples without local minima
Pierre Baldi and Kurt Hornik · 1989
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Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values
Pentti Paatero and Unto Tapper · 1994
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Independent component analysis: algorithms and applications
Aapo Hyvärinen and Erkki Oja · 2000
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Canonical correlation analysis: An overview with application to learning methods
David R. Hardoon, Sandor Szedmak, and John Shawe-Taylor · 2004
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Online dictionary learning for sparse coding
Julien Mairal, Francis Bach, Jean Ponce, and Guillermo Sapiro · 2009
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Principal component analysis
Ian Jolliffe · 2011
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Roger A. Horn and Charles R. Johnson · 2013
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Complete dictionary recovery over the sphere
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Escaping from saddle points? online stochastic gradient for tensor decomposition
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Nonconvex phase synchronization
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Deep learning without poor local minima
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Identity matters in deep learning
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Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
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The loss surface of deep and wide neural networks
Quynh Nguyen and Matthias Hein · 2017
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Learning one-hidden-layer neural networks with landscape design
Rong Ge, Jason D. Lee, and Tengyu Ma · 2017
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How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan · 2017
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On landscape of lagrangian functions and stochastic search for constrained nonconvex optimization
Zhehui Chen, Xingguo Li, Lin F. Yang, Jarvis Haupt, and Tuo Zhao · 2018
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On the stability of gradient flow dynamics for a rank-one matrix approximation problem
Hesameddin Mohammadi, Meisam Razaviyayn, and Mihailo R Jovanović · 2018
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Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2016
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Gradient descent only converges to minimizers
Jason D Lee, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2016
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 2017
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A geometric analysis of phase retrieval
Ju Sun, Qing Qu, and John Wright · 2018
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On the optimization of deep networks: Implicit acceleration by overparameterization
S. Arora, N. Cohen, and E. Hazan · 2018
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Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced
Simon S. Du, Wei Hu, and Jason D. Lee · 2018
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Symmetry, saddle points, and global optimization landscape of nonconvex matrix factorization
Xingguo Li, Junwei Lu, Raman Arora, Jarvis Haupt, Han Liu, Zhaoran Wang, and Tuo Zhao · 2019
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