Journal ArticleDOI
A principal component analysis algorithm with invariant norm
TLDR
It is proved rigorously that the continuous-time differential equations corresponding to this proposed PCA algorithm will converge to the principal eigenvectors of the autocorrelation matrix of the input signals with the norm of the initial weight vector.About:
This article is published in Neurocomputing.The article was published on 1995-07-01. It has received 23 citations till now. The article focuses on the topics: Sparse PCA & Principal component analysis.read more
Citations
More filters
Journal ArticleDOI
Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix
Zhang Yi,Yan Fu,Huajin Tang +2 more
TL;DR: This paper proposes a neural network based approach to compute eigenvectors corresponding to the largest or smallest eigenvalues of any real symmetric matrix and computer simulation results show the computational capability of the network model.
Journal ArticleDOI
Neural Network Implementations for PCA and Its Extensions
TL;DR: This paper gives an introduction to various neural network implementations and algorithms for principal component analysis (PCA), a statistical method that is directly related to EVD and SVD.
Journal ArticleDOI
Letter: A simple functional neural network for computing the largest and smallest eigenvalues and corresponding eigenvectors of a real symmetric matrix
TL;DR: This paper proposes a concise functional neural network expressed as a differential equation and designs steps to do this work, which can compute the smallest eigenvalue and the largest eigen value whether the matrix is non-definite, positive definite or negative definite.
Journal ArticleDOI
Letter: A functional neural network for computing the largest modulus eigenvalues and their corresponding eigenvectors of an anti-symmetric matrix
TL;DR: A functional neural network that can be transformed into a complex differential equation to do efficient computation of the largest modulus eigenvalues of a real anti-symmetric matrix is proposed.
Journal ArticleDOI
Letters: Recurrent neural network model for computing largest and smallest generalized eigenvalue
Lijun Liu,Hongmei Shao,Dong Nan +2 more
TL;DR: A continuous recurrent neural network model is presented for computing the largest and smallest generalized eigenvalue of a symmetric positive pair (A,B) and convergence properties to the extremum eigenvalues based upon Liapunov functional with the help of the generalized Eigen-decomposition theorem are obtained.
References
More filters
Journal ArticleDOI
Optimal Unsupervised Learning in a Single-Layer Linear Feedforward Neural Network
TL;DR: An optimality principle is proposed which is based upon preserving maximal information in the output units and an algorithm for unsupervised learning based upon a Hebbian learning rule, which achieves the desired optimality is presented.
Book
Neural networks for optimization and signal processing
A. Cochocki,Rolf Unbehauen +1 more
TL;DR: A guide to the fundamental mathematics of neurocomputing, a review of neural network models and an analysis of their associated algorithms, and state-of-the-art procedures to solve optimization problems are explained.
Journal ArticleDOI
Analysis of recursive stochastic algorithms
TL;DR: It is shown how a deterministic differential equation can be associated with the algorithm and examples of applications of the results to problems in identification and adaptive control.
Book
Stochastic Approximation Methods for Constrained and Unconstrained Systems
Harold J. Kushner,Dean S. Clark +1 more
TL;DR: In this paper, the authors present an algorithm for inequality constraints in a Dynamical System, based on the Robbins-Monro Process and Kiefer-Wolfowitz procedure. But they do not consider the case where the limit satisfies a Generalized ODE.
Journal ArticleDOI
Representation and separation of signals using nonlinear PCA type learning
Juha Karhunen,Jyrki Joutsensalo +1 more
TL;DR: A class of nonlinear PCA (principal component analysis) type learning algorithms is derived by minimizing a general statistical signal representation error and several known algorithms emerge as special cases of these optimization approaches that provide useful information on the properties of the algorithms.
Related Papers (5)
Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix
Zhang Yi,Yan Fu,Huajin Tang +2 more