NDLI: A Unified Self-Stabilizing Neural Network Algorithm for Principal and Minor Components Extraction

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A Unified Self-Stabilizing Neural Network Algorithm for Principal and Minor Components Extraction

Content Provider	IEEE Xplore Digital Library
Author	Xiangyu Kong Changhua Hu Hongguang Ma Chongzhao Han
Copyright Year	2012
Abstract	Recently, many unified learning algorithms have been developed for principal component analysis and minor component analysis. These unified algorithms can be used to extract principal components and, if altered simply by the sign, can also serve as a minor component extractor. This is of practical significance in the implementations of algorithms. This paper proposes a unified self-stabilizing neural network learning algorithm for principal and minor components extraction, and studies the stability of the proposed unified algorithm via the fixed-point analysis method. The proposed unified self-stabilizing algorithm for principal and minor components extraction is extended for tracking the principal subspace (PS) and minor subspace (MS). The averaging differential equation and the energy function associated with the unified algorithm for tracking PS and MS are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set, and the corresponding energy function exhibit a unique global minimum attained if and only if its state matrices span the PS or MS of the autocorrelation matrix of a vector data stream. It is concluded that the proposed unified algorithm for tracking PS and MS can efficiently track an orthonormal basis of the PS or MS. Simulations are carried out to further illustrate the theoretical results achieved.
Page Count	14
File Size	833852
Starting Page	185
Ending Page	198
File Format	PDF
ISSN	2162237X
Volume Number	23
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Principal component analysis Algorithm design and analysis Vectors Eigenvalues and eigenfunctions Cost function Neurons Convergence principal subspace Feature extraction learning algorithm minor component analysis minor subspace neural networks principal component analysis
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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