A stable MCA learning algorithm
Computers & Mathematics with Applications
A unified learning algorithm to extract principal and minor components
Digital Signal Processing
A Self-Stabilizing Neural Algorithm for Total Least Squares Filtering
Neural Processing Letters
Linear prediction based blind source extraction algorithms in practical applications
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
On the discrete-time dynamics of a class of self-stabilizing MCA extraction algorithms
IEEE Transactions on Neural Networks
A self-stabilizing MSA algorithm in high-dimension data stream
Neural Networks
Adaptive multiple minor directions extraction in parallel using a PCA neural network
Theoretical Computer Science
Convergence analysis for feng's MCA neural network learning algorithm
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
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A novel random-gradient-based algorithm is developed for online tracking the minor component (MC) associated with the smallest eigenvalue of the autocorrelation matrix of the input vector sequence. The five available learning algorithms for tracking one MC are extended to those for tracking multiple MCs or the minor subspace (MS). In order to overcome the dynamical divergence properties of some available random-gradient-based algorithms, we propose a modification of the Oja-type algorithms, called OJAm, which can work satisfactorily. The averaging differential equation and the energy function associated with the OJAm are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set. The corresponding energy or Lyapunov functions exhibit a unique global minimum attained if and only if its state matrices span the MS of the autocorrelation matrix of a vector data stream. The other stationary points are saddle (unstable) points. The globally convergence of OJAm is also studied. The OJAm provides an efficient online learning for tracking the MS. It can track an orthonormal basis of the MS while the other five available algorithms cannot track any orthonormal basis of the MS. The performances of the relative algorithms are shown via computer simulations.