Cross-correlation Neural Network Research Articles

Coupled cross-correlation neural network algorithm for principal singular triplet extraction of a cross-covariance matrix

This paper proposes a novel coupled neural network learning algorithm to extract the principal singular triplet (PST) of a cross-correlation matrix between two high-dimensional data streams. We firstly introduce a novel information criterion (NIC), in which the stationary points are singular triplet of the crosscorrelation matrix. Then, based on Newton's method, we obtain a coupled system of ordinary differential equations (ODEs) from the NIC. The ODEs have the same equilibria as the gradient of NIC, however, only the first PST of the system is stable (which is also the desired solution), and all others are (unstable) saddle points. Based on the system, we finally obtain a fast and stable algorithm for PST extraction. The proposed algorithm can solve the speed-stability problem that plagues most noncoupled learning rules. Moreover, the proposed algorithm can also be used to extract multiple PSTs effectively by using sequential method.

Neural blind beamformer for cyclostationary signals

A blind beamforming algorithm based on a neural network is presented according to the characteristic of cyclostationary signals. This method transforms the question of estimating beamformer weight vectors into the one of computing the SVD of the cross correlation matrix of array input signals and their frequency shift signals. A cross correlation neural network is introduced to compute the SVD of the cross correlation matrix so as to reduce the computational complexity and carry out the blind beamforming more efficiently. The improved cross-coupled Hebbian learning rule presented can make the weights of the neural network converge much fast. Therefore, it is more promising in the practical use. This method can restrain noise and interference. Simulation proves its correctness.

A Neural Network Learning for Adaptively Extracting Cross-Correlation Features Between Two High-Dimensional Data Streams

This paper proposes a novel cross-correlation neural network (CNN) model for finding the principal singular subspace of a cross-correlation matrix between two high-dimensional data streams. We introduce a novel nonquadratic criterion (NQC) for searching the optimum weights of two linear neural networks (LNN). The NQC exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix, respectively. The other stationary points of the NQC are (unstable) saddle points. We develop an adaptive algorithm based on the NQC for tracking the principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences. The NQC algorithm provides a fast online learning of the optimum weights for two LNN. The global asymptotic stability of the NQC algorithm is analyzed. The NQC algorithm has several key advantages such as faster convergence, which is illustrated through simulations.

Cross-correlation neural network models for the smallest singular component of general matrix

Abstract In this paper, we provide the theoretical foundation for a novel neural model to solve the smallest singular component of general matrix, on the basis of an extension of the Hebbian rule and a modification of cross-coupled Hebbian rule. This model can efficiently extract the singular-value component of the cross-correlation matrix of two stochastic signals. By Lasalle’s invariance principle and Lyapunov’s indirect method, we study the global asymptotic convergence of the networks to the first singular vectors of the cross-correlation matrix or non-squares matrix. A comparative study on the related neural networks shows that this neural network is efficient for computing the smallest singular component of general matrix. The novel model may have useful applications in solving the total least-squares problems in adaptive signal processing and image compressing.

Cross-correlation neural network models for the smallest singular component of general matrix

In this paper, we provide the theoretical foundation for a novel neural model to solve the smallest singular component of general matrix, on the basis of an extension of the Hebbian rule and a modification of cross-coupled Hebbian rule. This model can efficiently extract the singular-value component of the cross-correlation matrix of two stochastic signals. By Lasalle’s invariance principle and Lyapunov’s indirect method, we study the global asymptotic convergence of the networks to the first singular vectors of the cross-correlation matrix or non-squares matrix. A comparative study on the related neural networks shows that this neural network is efficient for computing the smallest singular component of general matrix. The novel model may have useful applications in solving the total least-squares problems in adaptive signal processing and image compressing.

Cross-correlation neural network models

In this paper we provide theoretical foundations for a new neural model for singular value decomposition based on an extension of the Hebbian learning rule called the cross-coupled Hebbian rule. The model is extracting the SVD of the cross-correlation matrix of two stochastic signals and is an extension on previous work on neural-network-related principal component analysis (PCA). We prove the asymptotic convergence of the network to the principal (normalized) singular vectors of the cross-correlation and we provide simulation results which suggest that the convergence is exponential. The new model may have useful applications in the problems of filtering for signal processing and signal detection.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>