Singular Feature Extraction and Its Neural Networks

From the preceding chapters, we have seen that in the wake of the important initiative work by Oja and Sanger, many neural network learning algorithms for PCA have been developed.

[1]  Stella Markantonatou,et al.  Applying the SOM Model to Text Classification According to Register and Stylistic Content , 2003, Int. J. Neural Syst..

[2]  Fa-Long Luo,et al.  Real-time computation of singular vectors , 1997 .

[3]  Heiko Hoffmann,et al.  An extension of neural gas to local PCA , 2004, Neurocomputing.

[4]  Fenghua Zhu,et al.  Traffic flow data forecasting based on interval type-2 fuzzy sets theory , 2016, IEEE/CAA Journal of Automatica Sinica.

[5]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[6]  R. Brockett Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems , 1991 .

[7]  Gen Hori,et al.  A general framework for SVD flows and joint SVD flows , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[8]  Qi Zhang,et al.  An Effective Neural Learning Algorithm for Extracting Cross-Correlation Feature Between Two High-Dimensional Data Streams , 2014, Neural Processing Letters.

[9]  Simone G. O. Fiori,et al.  Singular Value Decomposition Learning on Double Stiefel Manifold , 2003, Int. J. Neural Syst..

[10]  J. Bunch,et al.  Updating the singular value decomposition , 1978 .

[11]  John B. Moore,et al.  Singular-Value Decomposition via Gradient and Self-Equivalent Flows , 1992 .

[12]  D. M. Kammen,et al.  Quadrature and the development of orientation selective cortical cells by Hebb rules , 1989, Biological Cybernetics.

[13]  Ralf Möller,et al.  First-order approximation of Gram-Schmidt orthonormalization beats deflation in coupled PCA learning rules , 2006, Neurocomputing.

[14]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[15]  Sun-Yuan Kung,et al.  Cross-correlation neural network models , 1994, IEEE Trans. Signal Process..

[16]  Kurt Hornik,et al.  SVD Algorithms: APEX-like versus Subspace Methods , 2004, Neural Processing Letters.

[17]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[18]  Zheng Bao,et al.  A cross-associative neural network for SVD of non-squared data matrix in signal processing , 2001, IEEE Trans. Neural Networks.

[19]  Mohammed A. Hasan,et al.  Low-rank approximations with applications to principal singular component learning systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  Terence D. Sanger Two Iterative Algorithms for Computing the Singular Value Decomposition from Input/Output Samples , 1993, NIPS.

[21]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[22]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[23]  Thomas Kailath,et al.  ESPRIT-A subspace rotation approach to estimation of parameters of cisoids in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[24]  H. Hotelling Some New Methods in Matrix Calculation , 1943 .

[25]  John G. Proakis,et al.  Adaptive SVD algorithm for covariance matrix eigenstructure computation , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[26]  Ralf Möller,et al.  Coupled principal component analysis , 2004, IEEE Transactions on Neural Networks.

[27]  H. Hotelling Further Points on Matrix Calculation and Simultaneous Equations , 1943 .

[28]  Andrzej Cichocki,et al.  Neural network for singular value decomposition , 1992 .

[29]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.

[30]  Zheng Bao,et al.  A neural network learning for adaptively extracting cross-correlation features between two high-dimensional data streams , 2004, IEEE Transactions on Neural Networks.

[31]  Mohammed A. Hasan,et al.  A logarithmic cost function for principal singular component analysis , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[32]  Wolfram Schenck,et al.  Coupled Singular Value Decomposition of a Cross-Covariance Matrix , 2010, Int. J. Neural Syst..

[33]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[34]  Kurt Hornik,et al.  Learning in linear neural networks: a survey , 1995, IEEE Trans. Neural Networks.

[35]  Sun-Yuan Kung,et al.  Multilayer neural networks for reduced-rank approximation , 1994, IEEE Trans. Neural Networks.

[36]  Andrzej Cichocki,et al.  Neural networks for computing eigenvalues and eigenvectors , 1992, Biological Cybernetics.

[37]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[38]  Bin Yang,et al.  Projection approximation subspace tracking , 1995, IEEE Trans. Signal Process..

[39]  Nikola Samardzija,et al.  A neural network for computing eigenvectors and eigenvalues , 1991, Biological Cybernetics.

[40]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[41]  Xiaowei Feng,et al.  Coupled cross-correlation neural network algorithm for principal singular triplet extraction of a cross-covariance matrix , 2016, IEEE/CAA Journal of Automatica Sinica.

[42]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[43]  B. Noble Applied Linear Algebra , 1969 .

[44]  Gene H. Golub,et al.  Matrix computations , 1983 .

[45]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[46]  G. Golub,et al.  Tracking a few extreme singular values and vectors in signal processing , 1990, Proc. IEEE.

[47]  Chongzhao Han,et al.  A Dual Purpose Principal and Minor Subspace Gradient Flow , 2012, IEEE Transactions on Signal Processing.

[48]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

[49]  Steven T. Smith,et al.  Dynamical systems that perform the singular value decomposition , 1991 .

[50]  Joos Vandewalle,et al.  A Singular Value Decomposition Updating Algorithm for Subspace Tracking , 1992, SIAM J. Matrix Anal. Appl..