DocumentCode :
1399123
Title :
A Unified Self-Stabilizing Neural Network Algorithm for Principal and Minor Components Extraction
Author :
Xiangyu Kong ; Changhua Hu ; Hongguang Ma ; Chongzhao Han
Author_Institution :
Xi´an Res. Inst. of High Technol., Xi´an, China
Volume :
23
Issue :
2
fYear :
2012
Firstpage :
185
Lastpage :
198
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.
Keywords :
convergence; differential equations; learning (artificial intelligence); mathematics computing; matrix algebra; neural nets; principal component analysis; set theory; vectors; asymptotic converge; autocorrelation matrix; averaging differential equation; energy function; fixed-point analysis method; invariance set; minor component extraction; minor subspace; orthonormal basis; principal component analysis; principal component extraction; principal subspace; state matrix; unified learning algorithm; unified self-stabilizing neural network learning algorithm; vector data stream; Algorithm design and analysis; Convergence; Cost function; Eigenvalues and eigenfunctions; Neurons; Principal component analysis; Vectors; Feature extraction; learning algorithm minor component analysis; minor subspace; neural networks; principal component analysis; principal subspace;
fLanguage :
English
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
2162-237X
Type :
jour
DOI :
10.1109/TNNLS.2011.2178564
Filename :
6104232
Link To Document :
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