Neural networks Hopfield

Chapter 10 covers another important field with a great overlap with CA neural networks. Beginning with a short historical survey of what is really an independent field, chapter 10 discusses the Hopfield model, stochastic nets, Boltzman machines, and multi-layered perceptrons. 

While, as mentioned at the close of the last section, it took more than 15 years following Minsky and Papert s criticism of simple perceptrons for a bona-fide multilayered variant to finally emerge (see Multi-layeved Perceptrons below), the man most responsible for bringing respectability back to neural net research was the physicist John J, Hopfield, with the publication of his landmark 1982 paper entitled Neural networks and physical systems with emergent collective computational abilities [hopf82]. To set the stage for our discussion of Hopfield nets, we first pause to introduce the notion of associative memory. 

T. Kohonen, Self Organization and Associated Memory. Springer-Verlag, Heidelberg, 1989. W.J. Meissen, J.R.M. Smits, L.M.C. Buydens and G. Kateman, Using artificial neural networks for solving chemical problems. II. Kohonen self-organizing feature maps and Hopfield networks. Chemom. Intell. Lab. Syst., 23 (1994) 267-291. 

In analytical chemistry, Artificial Neural Networks (ANN) are mostly used for calibration, see Sect. 6.5, and classification problems. On the other hand, feedback networks are usefully to apply for optimization problems, especially nets ofHoPFiELD type (Hopfield [1982] Lee and Sheu [1990]). 

Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci USA 79 2554... 

Lee BW, Sheu BJ (1990) Combinatorial optimization using competitive Hopfield neural network. Proc Internat Joint Conf Neural Networks II 627, Washington, DC... 

Novel Alignment Method of Small Molecules Using the Hopfield Neural Network. 

Some historically important artificial neural networks are Hopfield Networks, Per-ceptron Networks and Adaline Networks, while the most well-known are Backpropa-gation Artificial Neural Networks (BP-ANN), Kohonen Networks (K-ANN, or Self-Organizing Maps, SOM), Radial Basis Function Networks (RBFN), Probabilistic Neural Networks (PNN), Generalized Regression Neural Networks (GRNN), Learning Vector Quantization Networks (LVQ), and Adaptive Bidirectional Associative Memory (ABAM). 

Hopfield networks [18] are able to store patterns as point attractors in n dimensional binary space and recall them in response to partial or degraded versions of stored patterns. For this reason, they are known as content addressable memories where each memory is a point attractor for nearby, similar patterns. Traditionally, known patterns are loaded directly into the network (see the learning rule 10 below), but in this paper we investigate the use of a Hopfield network to discover point attractors by sampling from a fitness function. A Hopfield network is a neural network consisting of n simple connected processing units. The values the units take are represented by a vector, u ... 

We define a Hopfield EDA (HEDA) as an EDA implemented by means of a Hopfield neural network. This section describes the training and use of a HEDA. Figure 2 shows a four neuron HEDA with the units labelled Wj and weights in one direction labelled Wi,. 

Liu sheng, Liu Na, Yang Yu. 2013. Safety evaluation of hazards based on discrete Hopfield neural network Journal of Chongqing University (Natural Science Edition) 36 26—32. 

The term neural network was traditionally used to refer to a network or circuit of biological neurons (Hopfield 1982). Modem usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes. Thus, the term has two distinct usages ... 

An important aspect that did come forward in the 1970s was that of self-organizing maps (SOMs). SOMs will be discussed later in this encyclopedia. In 1982, John Hopfield of Caltech presented a paper to the scientific community in which he stated that the approach to AI should not be to purely imitate the human brain but instead to use its concepts to buUd machines that could solve dynamic problems. He showed what such networks were capable of and how they would work. It was his articulate, likable character and his vast knowledge of mathematical analysis that convinced scientists and researchers at the National Academy of Sciences to renew interest into the research of AI and neural networks. His ideas gave birth to a new class of neural networks that over time became known as the Hopfield model. 

J. Hopfield, Proc. Natl. Acad. Sci. USA, 79, 2554 (1982). Neural Networks and Physical... 

H. Schulz, M. Derrick, and D. Stulik, Ana/. Chim. Acta, 316,145 (1995). Simple Encoding of Infrared Spectra for Pattern Recognition. 2. Neural Network Approach Using Back-Propagation and Associative Hopfield Memory. 

There is nothing like the neural network . Many types of neural networks have been proposed and used for various purposes, like Hopfield networks,the adaptive bidirectional associative memory,the Kohonen network, and radial basis funetion For the con-... 

FeuiUeaubois, E., Fabart, V., and Doucet, J. P. (1993) Implementation of the three-dimensional-pattern search problem on Hopfield-like neural networks. SAR QSAR Environ. Res. 1, 97-114. 

More than 50 different types of neural network exist. Certain networks are more efficient in optimization others perform better in data modeling and so forth. According to Basheer (2000) the most popular neural networks today are the Hopfield networks, the Adaptive Resonance Theory (ART) networks, the Kohonen networks, the counter propagation networks, the Radial Basis Function (RBF) networks, the backpropagation networks and recurrent networks. 

Buscono-Calzon, C. and Figueiras-Vidal, A.R. (1997) A bank of Hopfield neural networks for the shortest path problem. Journal of Computational and Applied Mathematics, 82 (1-2), 117-128. 

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