NDLI: Algorithms for accelerated convergence of adaptive PCA

Content Provider	IEEE Xplore Digital Library
Author	Chatterjee, C. Kang, Z. Roychowdhury, V.P.
Copyright Year	1990
Abstract	We derive and discuss adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja and Karhunen (1985), Sanger (1989), and Xu (1993). It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: (1) gradient descent; (2) steepest descent; (3) conjugate direction; and (4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods. We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	338
Ending Page	355
Page Count	18
File Size	524685
File Format	PDF
ISSN	10459227
Volume Number	11
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-03-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Acceleration Convergence Principal component analysis Signal processing algorithms Adaptive algorithm Algorithm design and analysis Multiple signal classification Direction of arrival estimation Frequency estimation Approximation algorithms
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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