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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Published in:	IEEE transaction on neural networks and learning systems Vol. 35; no. 5; pp. 7035 - 7047
Main Authors:	Le Thi, Hoai An, Luu, Hoang Phuc Hau, Dinh, Tao Pham
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.05.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	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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Abstract	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).
AbstractList	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).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). 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).
Author	Dinh, Tao Pham Le Thi, Hoai An Luu, Hoang Phuc Hau
Author_xml	– sequence: 1 givenname: Hoai An orcidid: 0000-0002-2239-2100 surname: Le Thi fullname: Le Thi, Hoai An email: hoai-an.le-thi@univ-lorraine.fr organization: Université de Lorraine, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Metz, France – sequence: 2 givenname: Hoang Phuc Hau orcidid: 0000-0003-0908-9817 surname: Luu fullname: Luu, Hoang Phuc Hau email: hoang-phuc-hau.luu@univ-lorraine.fr organization: Université de Lorraine, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Metz, France – sequence: 3 givenname: Tao Pham surname: Dinh fullname: Dinh, Tao Pham email: pham@insa-rouen.fr organization: Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen, University of Normandie, Saint-Étienne-du-Rouvray, France
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SubjectTerms	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
Title	Online Stochastic DCA With Applications to Principal Component Analysis
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