This second part of a Tutorial on neural networks focuses on the Kohonen self-organising feature map and the Hopfield network. First a theoretical description of each type is given. The practical issues concerning applications of the networks are then discussed. For each network, a description is given of the types of problems which can be tackled by the specific neural network, followed by a p...

In contradiction with Hopfield-like networks, random recurrent neural networks (RRNN), where the couplings are random, exhibit complex dynamics (limit cycles, chaos). It is possible to store information in these networks through hebbian learning. Eventually, learning “destroys” the dynamics and leads to a fixed point attractor. We investigate here the structural change in the networks through l...

This paper proposes a novel method based on Hopfield neural networks (HNNs) for solving job-shop scheduling problems (JSPs). The JSP constraints are analyzed and their permutation matrix express is developed. A new calculation energy function is also proposed, which includes all JSP constraints. A novel Hopfield neural network for such JSP problems is constructed and the effect of its weights f...

In this paper, the qualitative theory of large-scale dynamical systems is surveyed. In particular, the focus is the Hopfield Neural networks both with and without perturbations. Properties relating to asymptotic and exponential stability and instability are detailed. A model reduction technique based on balanced truncation is applied to the neural networks. Its effect on the stability propertie...

These days we can get massive information and it is hard to deal with it without computers. Machine learning is effective for computers to manage massive information. Machine learning uses various learning machine models, for instance, decision trees, Bayesian Networks, Support Vector Machine, Hidden Markov Model, normal mixed distributions, neural networks and so on. Some of them are stochasti...

Many neural network architectures operate only on real data and simple complex inputs. But there are applications where considerations of complex and quaternion inputs are quite desirable. Prior complex neural network models have generalized the Hopfield model, backpropagation and the perceptron learning rule to handle complex inputs. The Hopfield model for inputs and outputs falling on the uni...

In this paper a novel multi-user receiver is introduced, which unites fast convergence of neural networks with the asymptotically global optimization power of stochastic algorithms (e.g. Boltzmann machines). The proposed method is capable to achieve a 1..2 dB gain in performance over the traditional Hopfield neural network, while only 2 or 3 times more iterations is needed, which still does not...

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead ...

This work evaluates two artificial intelligence techniques for file distribution in Grid environments. These techniques are used to access data on independent servers in parallel, in order to improve the performance and maximize the throughput rate. In this work, genetic algorithms and Hopfield neural networks are the techniques used to solve the problem. Both techniques are evaluated for effic...

In this note, I review some basic properties of the Hopfield model. I closely follow Chapter 2 of Herz, Krogh & Palmer (1991) which is an excellent introductory textbook on the theory of neural networks. I motivate the mean field analysis of the stochastic Hopfield model slightly differently than Herz, Krogh & Palmer (1991) and my derivations are a little longer, filling in some of the gaps in ...