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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.3 P.298-304

http://doi.org/10.1631/jzus.2002.0298


Principal component analysis using neural network


Author(s):  YANG Jian-gang, SUN Bin-qiang

Affiliation(s):  Department of Computer Science & Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   yangjg@cs.zju.edu.cn

Key Words:  PCA, Unsymmetrical real matrix, Eigenvalue, Eigenvector, Neural network


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YANG Jian-gang, SUN Bin-qiang. Principal component analysis using neural network[J]. Journal of Zhejiang University Science A, 2002, 3(3): 298-304.

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author="YANG Jian-gang, SUN Bin-qiang",
journal="Journal of Zhejiang University Science A",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0298"
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T1 - Principal component analysis using neural network
A1 - YANG Jian-gang
A1 - SUN Bin-qiang
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EP - 304
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Abstract: 
The authors present their analysis of the differential equation dX(t)/dt=AX(t)-XT(t)BX(t)X(t), where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X∈Rn; showing that the equation characterizes a class of continuous type full-feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X0∈Rn, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non-positive. 2. For any initial value X0 outside a proper subspace of Rn, the solution approximates asymptotically to a nontrivial constant vector &Ytilde;(X0). In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X0)‖2B and (X0) is the corresponding eigenvector. 3. For any initial value X0 outside a proper subspace of Rn, the solution approximates asymptotically to a non-constant periodic function &Ytilde;(X0,t). Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.

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Reference

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