Online Stochastic DCA With Applications to Principal Component Analysis

Stochastic algorithms are well-known for their performance in the era of big data. In this article, we study nonsmooth stochastic Difference-of-Convex functions (DC) programs-the major class of nonconvex stochastic optimization, which have a variety of applications in divers domains, in particular,...

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Veröffentlicht in:IEEE transaction on neural networks and learning systems Jg. 35; H. 5; S. 7035 - 7047
Hauptverfasser: Le Thi, Hoai An, Luu, Hoang Phuc Hau, Dinh, Tao Pham
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.05.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Big Data
Computer Science
Convex functions
DC~algorithm (DCA)
Difference of Convex functions (DC) programming
Divers
Learning algorithms
Machine learning
Machine learning algorithms
Martingales
Mathematics
nonconvex optimization
online stochastic DCA (osDCA)
Optimization
Principal component analysis
principal component analysis (PCA)
Principal components analysis
Programming
Stochastic processes
Stochasticity
Difference of Convex functions (DC) programming
Online stochastic DCA (osDCA)
DC algorithm (DCA)
Nonconvex optimization
Principal component analysis (PCA)
ISSN:2162-237X, 2162-2388, 2162-2388
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Zusammenfassung:Stochastic algorithms are well-known for their performance in the era of big data. In this article, we study nonsmooth stochastic Difference-of-Convex functions (DC) programs-the major class of nonconvex stochastic optimization, which have a variety of applications in divers domains, in particular, machine learning. We propose new online stochastic algorithms based on the state-of-the-art DC Algorithm (DCA)-a powerful approach in nonconvex programming framework, in the online context of streaming data continuously generated by some (unknown) source distribution. The new schemes use the stochastic approximations (SAs) principle: deterministic quantities of the standard DCA are replaced by their noisy estimators constructed using newly arriving samples. The convergence analysis of the proposed algorithms is studied intensively with the help of tools from modern convex analysis and martingale theory. Finally, we study several aspects of the proposed algorithms on an important problem in machine learning: the expected problem in principal component analysis (PCA).
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2022.3213558