Neural Learning on Grassman/Stiefel Principal/Minor Submanifold

This paper proposes a generalization of the recently proposed method that transforms known neural network PSA/MSA algorithms, into PCA/MCA algorithms. The method uses two distinct time scales. A given PSA/MSA algorithm is responsible, on a faster time scale, for the "behavior" of all outpu...

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Bibliographic Details
Main Authors: Jankovic, M.V., Reljin, B.
Format: Conference Proceeding
Language:English
Subjects:
Array signal processing
Computational modeling
Curve fitting
Grassman manifold
Independent component analysis
Mathematical analysis
MCA
MSA
Neural networks
Neurons
PCA
Principal component analysis
PSA
Stiefel manifold
Surface fitting
Vectors
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Description
Summary:This paper proposes a generalization of the recently proposed method that transforms known neural network PSA/MSA algorithms, into PCA/MCA algorithms. The method uses two distinct time scales. A given PSA/MSA algorithm is responsible, on a faster time scale, for the "behavior" of all output neurons. At this scale principal/minor subspace is obtained. On a slower time scale, output neurons compete to fulfil their "own interests". On this scale, basis vectors in the principal/minor subspace are rotated toward the principal/minor eigenvectors. Actually, time-oriented hierarchical method is proposed. Some simplified mathematical analysis, as well as simulation results, are presented
DOI:10.1109/EURCON.2005.1629907