Share on Facebook Share on Twitter Email
Answers.com

neural network

Did you mean: neural network (in computers, electronics), Neural Networks (journal)

 
Dictionary: neural network
also neural net
n.
A real or virtual device, modeled after the human brain, in which several interconnected elements process information simultaneously, adapting and learning from past patterns.


Search unanswered questions...
Enter a question here...
Search: All sources Community Q&A Reference topics

Type of parallel computation in which computing elements are modeled on the network of neurons that constitute animal nervous systems. This model, intended to simulate the way the brain processes information, enables the computer to "learn" to a certain degree. A neural network typically consists of a number of interconnected processors, or nodes. Each handles a designated sphere of knowledge, and has several inputs and one output to the network. Based on the inputs it gets, a node can "learn" about the relationships between sets of data, sometimes using the principles of fuzzy logic. For example, a backgammon program can store and grade results from moves in a game; in the next game, it can play a move based on its stored result and can regrade the stored result if the move is unsuccessful. Neural networks have been used in pattern recognition, speech analysis, oil exploration, weather prediction, and the modeling of thinking and consciousness.

For more information on neural network, visit Britannica.com.

Sci-Tech Encyclopedia: Neural network
Top

An information-processing device that consists of a large number of simple nonlinear processing modules, connected by elements that have information storage and programming functions. The field of neural networks is an emerging technology in the area of machine information processing and decision making. The main thrusts are toward highly innovative machine and algorithmic architectures, radically different from those that have been employed in conventional digital computers. The information-processing elements and components of neural networks, inspired by neuroscientific studies of the structure and function of the human brain, are conceptually simple. Three broad categories of neural-network architectures have been formulated which exhibit highly complex information-processing capabilities. Several generic models have been advanced which offer distinct advantages over traditional digital-computer implementation. Neural networks have created an unusual amount of interest in the engineering and industrial communities by opening up new research directions and commercial and military applications. See also Neurobiology.

Automated information processing is achieved by means of modules that in general involve four functions: input/output (getting in and out of the machine), processing (executing prescribed specific information-handling tasks), memory (storing information), and connections between different modules providing for information flow and control. Neural networks contain a very large number of simple processing modules. This contrasts with traditional digital computers, which contain a small number of complex processing modules that are rather sophisticated in the sense that they are capable of executing very large sets of prescribed arithmetic and logical tasks (instructions). In conventional digital computers, the four functions listed above are carried out by separate dedicated machine units. In neural networks information storage is achieved by components which at the same time effect connections between distinct machine units. These key distinctions between the neural-network and the digital computer architectures are of a fundamental nature and have major implications in machine design and in machine utilization.

The information-processing properties of neural networks depend mainly on two factors: the network topology (the scheme used to connect elements or nodes together), and the algorithm (the rules) employed to specify the values of the weights connecting the nodes. While the ultimate configuration and parameter values are problem-specific, it is possible to classify neural networks, on the basis of how information is stored or retrieved, in four broad categories: neural networks behaving as learning machines with a teacher; neural networks behaving as learning machines without a teacher; neural networks behaving as associative memories; and neural networks that contain analog as well as digital devices and result in hybrid-machine implementations that integrate complex continuous dynamic processing and logical functions. Within these four categories, several generic models have found important applications, and still others are under intensive investigation.

Neural-network research is developing a new conceptual framework for representing and utilizing information, which will result in a significant advance in information epistemology. Communication technology is based on the notions of coding and channel capacity (bits per second), which provide the conceptual framework for information representation appropriate to machine-based communication. Neural-network systems (biological or artificial) do not store information or process it in the way that conventional digital computers do. Specifically, the basic unit of neural-network operation is not based on the notion of the instruction but on the connection. The performance of a neural network depends directly on the number of connections per second that it effects, and thus its performance is better understood in terms of its connections-per-second (CPS) capability. See also Information theory.


Modern Science: neural network
Top
neural networks

A computer system that is designed to mimic the human brain or some other biological system in its functioning. They were developed to deal with problems, like pattern recognition, that the brain does well but that traditional computer systems cannot handle easily.

Computer Desktop Encyclopedia: neural network
Top

A modeling technique based on the observed behavior of biological neurons and used to mimic the performance of a system. It consists of a set of elements that start out connected in a random pattern, and, based upon operational feedback, are molded into the pattern required to generate the required results. It is used in applications such as robotics, diagnosing, forecasting, image processing and pattern recognition.

Download Computer Desktop Encyclopedia to your iPhone/iTouch

Investment Dictionary: Neural Network
Top

A series of algorithms that attempt to identify underlying relationships in a set of data by using a process that mimics the way the human brain operates. Neural networks have the ability to adapt to changing input so that the network produces the best possible result without the need to redesign the output criteria.

Investopedia Says:
The concept of neural networks is rapidly increasing in popularity in the area of developing trading systems. At one point in time, it would have seemed impossible to make a system that would be able to adapt to changing markets, but recent developments in technology have now made having these types of systems a reality.

Related Links:
Take a look at the algorithmic approach to technical trading - you may never go back! Train To Gain With Neural Networks
Is it possible for applications simulating the human brain to make better trading decisions? Neural Trading: Biological Keys to Profit
Automate your trades by translating your strategy into a language your computer can implement in this hands-free approach to investing. Trading Systems Coding
A trading system can save time and take the emotion out of trading, but adopting one takes skill and resources - learn more here. Basics Of Trading Systems


Accounting Dictionary: Neural Networks
Top

Technology in which computers actually try to learn from the data base and operator what the right answer is to a question. The system gets positive or negative response to output from the operator and stores that data so that it will make a better decision the next time. While still in its infancy, this technology shows promise for use in accounting, fraud detection, economic forecasting, and risk appraisals. The idea behind this software is to convert the order-taking computer into a "thinking" problem solver.

Geography Dictionary: neural networks
Top

Computer systems which deal with data by the use of simple processors, whose output is then entered into a second layer of processors, and so on through several layers. These networks can throw up pragmatic, rather than theory-based, models, thus producing new insights; for example, neural networks have been used to develop a classification of land use, based on images from remote sensors. They can work on limited data, and are flexible; new connections can be made with the input of further data. See also algorithms.

 
Columbia Encyclopedia: neural network
Top
neural network or neural computing, computer architecture modeled upon the human brain's interconnected system of neurons. Neural networks imitate the brain's ability to sort out patterns and learn from trial and error, discerning and extracting the relationships that underlie the data with which it is presented. Most neural networks are software simulations run on conventional computers. In neural computers, transistor circuits serve as the neurons and variable resistors act as the interconnection between axons and dendrites (see nervous system). A neural network on an integrated circuit, with 1,024 silicon "neurons," has also been developed. Each neuron in the network has one or more inputs and produces an output; each input has a weighting factor, which modifies the value entering the neuron. The neuron mathematically manipulates the inputs, and outputs the result. The neural network is simply neurons joined together, with the output from one neuron becoming input to others until the final output is reached. The network learns when examples (with known results) are presented to it; the weighting factors are adjusted-either through human intervention or by a programmed algorithm-to bring the final output closer to the known result.

Neural networks are good at providing very fast, very close approximations of the correct answer. Although they are not as well suited as conventional computers for performing mathematical calculations or moving and comparing alphabetic characters, neural networks excel at recognizing shapes or patterns, learning from experience, or sorting relevant data from irrelevant. Their applications can be categorized into classification, recognition and identification, assessment, monitoring and control, and forecasting and prediction. Among the tasks for which they are well suited are handwriting recognition, foreign language translation, process control, financial forecasting, medical data interpretation, artificial intelligence research, and parallel processing implementations of conventional processing tasks. In an ironic reversal, neural networks are being used to model disorders of the brain in an effort to discover better therapeutic strategies.

Bibliography

See Y. Burnod, An Adaptive Neural Network: The Cerebral Cortex (1990); J. S. Judd, Neural Network Design and the Complexity of Learning (1990); S. I. Gallant, Neural Network Learning and Expert Systems (1993); L. Medsker, Hybrid Neural Network and Expert Systems (1994); R. L. Harvey, Neural Network Principles (1994).


Wikipedia: Neural network
Top
Simplified view of a feedforward artificial neural network

Traditionally, the term neural network had been used to refer to a network or circuit of biological neurons[citation needed]. The modern 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:

  1. Biological neural networks are made up of real biological neurons that are connected or functionally related in the peripheral nervous system or the central nervous system. In the field of neuroscience, they are often identified as groups of neurons that perform a specific physiological function in laboratory analysis.
  2. Artificial neural networks are made up of interconnecting artificial neurons (programming constructs that mimic the properties of biological neurons). Artificial neural networks may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system. The real, biological nervous system is highly complex and includes some features that may seem superfluous based on an understanding of artificial networks.

This article focuses on the relationship between the two concepts; for detailed coverage of the two different concepts refer to the separate articles: Biological neural network and Artificial neural network.

Contents

Overview

In general a biological neural network is composed of a group or groups of chemically connected or functionally associated neurons. A single neuron may be connected to many other neurons and the total number of neurons and connections in a network may be extensive. Connections, called synapses, are usually formed from axons to dendrites, though dendrodendritic microcircuits[1] and other connections are possible. Apart from the electrical signaling, there are other forms of signaling that arise from neurotransmitter diffusion, which have an effect on electrical signaling. As such, neural networks are extremely complex.

Artificial intelligence and cognitive modeling try to simulate some properties of neural networks. While similar in their techniques, the former has the aim of solving particular tasks, while the latter aims to build mathematical models of biological neural systems.

In the artificial intelligence field, artificial neural networks have been applied successfully to speech recognition, image analysis and adaptive control, in order to construct software agents (in computer and video games) or autonomous robots. Most of the currently employed artificial neural networks for artificial intelligence are based on statistical estimation, optimization and control theory.

The cognitive modelling field involves the physical or mathematical modeling of the behaviour of neural systems; ranging from the individual neural level (e.g. modelling the spike response curves of neurons to a stimulus), through the neural cluster level (e.g. modelling the release and effects of dopamine in the basal ganglia) to the complete organism (e.g. behavioural modelling of the organism's response to stimuli).

History of the neural network analogy

The concept neural networks started in the late-1800s as an effort to describe how the human mind performed. These ideas started being applied to computational models with Turing's B-type machines and the perceptron.

In early 1950s Friedrich Hayek was one of the first to posit the idea of spontaneous order[citation needed] in the brain arising out of decentralized networks of simple units (neurons). In the late 1940s, Donald Hebb made one of the first hypotheses for a mechanism of neural plasticity (i.e. learning), Hebbian learning. Hebbian learning is considered to be a 'typical' unsupervised learning rule and it (and variants of it) was an early model for long term potentiation.

The perceptron is essentially a linear classifier for classifying data  x \in R^n specified by parameters w \in R^n, b \in R and an output function f = w'x + b. Its parameters are adapted with an ad-hoc rule similar to stochastic steepest gradient descent. Because the inner product is a linear operator in the input space, the Perceptron can only perfectly classify a set of data for which different classes are linearly separable in the input space, while it often fails completely for non-separable data. While the development of the algorithm initially generated some enthusiasm, partly because of its apparent relation to biological mechanisms, the later discovery of this inadequacy caused such models to be abandoned until the introduction of non-linear models into the field.

The cognitron (1975) was an early multilayered neural network with a training algorithm. The actual structure of the network and the methods used to set the interconnection weights change from one neural strategy to another, each with its advantages and disadvantages. Networks can propagate information in one direction only, or they can bounce back and forth until self-activation at a node occurs and the network settles on a final state. The ability for bi-directional flow of inputs between neurons/nodes was produced with the Hopfield's network (1982), and specialization of these node layers for specific purposes was introduced through the first hybrid network.

The parallel distributed processing of the mid-1980s became popular under the name connectionism.

The rediscovery of the backpropagation algorithm was probably the main reason behind the repopularisation of neural networks after the publication of "Learning Internal Representations by Error Propagation" in 1986 (Though backpropagation itself dates from 1974). The original network utilised multiple layers of weight-sum units of the type f = g(w'x + b), where g was a sigmoid function or logistic function such as used in logistic regression. Training was done by a form of stochastic steepest gradient descent. The employment of the chain rule of differentiation in deriving the appropriate parameter updates results in an algorithm that seems to 'backpropagate errors', hence the nomenclature. However it is essentially a form of gradient descent. Determining the optimal parameters in a model of this type is not trivial, and steepest gradient descent methods cannot be relied upon to give the solution without a good starting point. In recent times, networks with the same architecture as the backpropagation network are referred to as Multi-Layer Perceptrons. This name does not impose any limitations on the type of algorithm used for learning.

The backpropagation network generated much enthusiasm at the time and there was much controversy about whether such learning could be implemented in the brain or not, partly because a mechanism for reverse signalling was not obvious at the time, but most importantly because there was no plausible source for the 'teaching' or 'target' signal.

The brain, neural networks and computers

Neural networks, as used in artificial intelligence, have traditionally been viewed as simplified models of neural processing in the brain, even though the relation between this model and brain biological architecture is debated[citation needed].

A subject of current research in theoretical neuroscience is the question surrounding the degree of complexity and the properties that individual neural elements should have to reproduce something resembling animal intelligence.

Historically, computers evolved from the von Neumann architecture, which is based on sequential processing and execution of explicit instructions. On the other hand, the origins of neural networks are based on efforts to model information processing in biological systems, which may rely largely on parallel processing as well as implicit instructions based on recognition of patterns of 'sensory' input from external sources. In other words, at its very heart a neural network is a complex statistical processor (as opposed to being tasked to sequentially process and execute).

Neural networks and artificial intelligence

An artificial neural network (ANN), also called a simulated neural network (SNN) or commonly just neural network (NN) is an interconnected group of artificial neurons that uses a mathematical or computational model for information processing based on a connectionistic approach to computation. In most cases an ANN is an adaptive system that changes its structure based on external or internal information that flows through the network.

In more practical terms neural networks are non-linear statistical data modeling or decision making tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data.

Background

An artificial neural network involves a network of simple processing elements (artificial neurons) which can exhibit complex global behavior, determined by the connections between the processing elements and element parameters. Artificial neurons were first proposed in 1943 by Warren McCulloch, a neurophysiologist, and Walter Pitts, an MIT logician.[1] One classical type of artificial neural network is the recurrent Hopfield net.

In a neural network model simple nodes, which can be called variously "neurons", "neurodes", "Processing Elements" (PE) or "units", are connected together to form a network of nodes — hence the term "neural network". While a neural network does not have to be adaptive per se, its practical use comes with algorithms designed to alter the strength (weights) of the connections in the network to produce a desired signal flow.

In modern software implementations of artificial neural networks the approach inspired by biology has more or less been abandoned for a more practical approach based on statistics and signal processing. In some of these systems, neural networks, or parts of neural networks (such as artificial neurons), are used as components in larger systems that combine both adaptive and non-adaptive elements.

The concept of a neural network appears to have first been proposed by Alan Turing in his 1948 paper "Intelligent Machinery".

Applications

The utility of artificial neural network models lies in the fact that they can be used to infer a function from observations and also to use it. This is particularly useful in applications where the complexity of the data or task makes the design of such a function by hand impractical.

Real life applications

The tasks to which artificial neural networks are applied tend to fall within the following broad categories:

Application areas include system identification and control (vehicle control, process control), game-playing and decision making (backgammon, chess, racing), pattern recognition (radar systems, face identification, object recognition, etc.), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications, data mining (or knowledge discovery in databases, "KDD"), visualization and e-mail spam filtering.

Use in Teaching Strategy

Neural Networks are being used to determine the significance of a seating arrangement in a classroom learning environment. In this application, neural networks have proven that there is a correlation between the location of high and low-performing students in the room and how well they do in the class. An article in Complexity explains that when low-performing students are seated in the front, their chance to do better increases. The results of high-performing students who are seated in the back are not affected. In addition, when high-performing students are seated in the outer four corners, the performance of the class as a whole increases. [2][2]

Neural network software

Main article: Neural network software

Neural network software is used to simulate, research, develop and apply artificial neural networks, biological neural networks and in some cases a wider array of adaptive systems.

Learning paradigms

There are three major learning paradigms, each corresponding to a particular abstract learning task. These are supervised learning, unsupervised learning and reinforcement learning. Usually any given type of network architecture can be employed in any of those tasks.

Supervised learning

In supervised learning, we are given a set of example pairs  (x, y), x \in X, y \in Y and the aim is to find a function f in the allowed class of functions that matches the examples. In other words, we wish to infer how the mapping implied by the data and the cost function is related to the mismatch between our mapping and the data.

Unsupervised learning

In unsupervised learning we are given some data x, and a cost function which is to be minimized which can be any function of x and the network's output, f. The cost function is determined by the task formulation. Most applications fall within the domain of estimation problems such as statistical modeling, compression, filtering, blind source separation and clustering.

Reinforcement learning

In reinforcement learning, data x is usually not given, but generated by an agent's interactions with the environment. At each point in time t, the agent performs an action yt and the environment generates an observation xt and an instantaneous cost ct, according to some (usually unknown) dynamics. The aim is to discover a policy for selecting actions that minimizes some measure of a long-term cost, i.e. the expected cumulative cost. The environment's dynamics and the long-term cost for each policy are usually unknown, but can be estimated. ANNs are frequently used in reinforcement learning as part of the overall algorithm. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

Learning algorithms

There are many algorithms for training neural networks; most of them can be viewed as a straightforward application of optimization theory and statistical estimation. They include: Back propagation by gradient descent, Rprop, BFGS, CG etc.

Evolutionary computation methods, simulated annealing, expectation maximization and non-parametric methods are among other commonly used methods for training neural networks. See also machine learning.

Recent developments in this field also saw the use of particle swarm optimization and other swarm intelligence techniques used in the training of neural networks.

Neural networks and neuroscience

Theoretical and computational neuroscience is the field concerned with the theoretical analysis and computational modeling of biological neural systems. Since neural systems are intimately related to cognitive processes and behaviour, the field is closely related to cognitive and behavioural modeling.

The aim of the field is to create models of biological neural systems in order to understand how biological systems work. To gain this understanding, neuroscientists strive to make a link between observed biological processes (data), biologically plausible mechanisms for neural processing and learning (biological neural network models) and theory (statistical learning theory and information theory).

Types of models

Many models are used in the field, each defined at a different level of abstraction and trying to model different aspects of neural systems. They range from models of the short-term behaviour of individual neurons, through models of how the dynamics of neural circuitry arise from interactions between individual neurons, to models of how behaviour can arise from abstract neural modules that represent complete subsystems. These include models of the long-term and short-term plasticity of neural systems and its relation to learning and memory, from the individual neuron to the system level.

Current research

While initially research had been concerned mostly with the electrical characteristics of neurons, a particularly important part of the investigation in recent years has been the exploration of the role of neuromodulators such as dopamine, acetylcholine, and serotonin on behaviour and learning.

Biophysical models, such as BCM theory, have been important in understanding mechanisms for synaptic plasticity, and have had applications in both computer science and neuroscience. Research is ongoing in understanding the computational algorithms used in the brain, with some recent biological evidence for radial basis networks and neural backpropagation as mechanisms for processing data.

Criticism

A common criticism of neural networks, particularly in robotics, is that they require a large diversity of training for real-world operation. Dean Pomerleau, in his research presented in the paper "Knowledge-based Training of Artificial Neural Networks for Autonomous Robot Driving," uses a neural network to train a robotic vehicle to drive on multiple types of roads (single lane, multi-lane, dirt, etc.). A large amount of his research is devoted to (1) extrapolating multiple training scenarios from a single training experience, and (2) preserving past training diversity so that the system does not become overtrained (if, for example, it is presented with a series of right turns – it should not learn to always turn right). These issues are common in neural networks that must decide from amongst a wide variety of responses.

A. K. Dewdney, a former Scientific American columnist, wrote in 1997, "Although neural nets do solve a few toy problems, their powers of computation are so limited that I am surprised anyone takes them seriously as a general problem-solving tool." (Dewdney, p. 82)

Arguments for Dewdney's position are that to implement large and effective software neural networks, much processing and storage resources need to be committed. While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a most simplified form on Von Neumann technology may compel a NN designer to fill many millions of database rows for its connections - which can lead to abusive RAM and HD necessities. Furthermore, the designer of NN systems will often need to simulate the transmission of signals through many of these connections and their associated neurons - which must often be matched with incredible amounts of CPU processing power and time. While neural networks often yield effective programs, they too often do so at the cost of time and money efficiency.

Arguments against Dewdney's position are that neural nets have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft[3] to detecting credit card fraud[4].

Technology writer Roger Bridgman commented on Dewdney's statements about neural nets:

Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource". In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.[3]

Some other criticisms came from believers of hybrid models (combining neural networks and symbolic approaches). They advocate the intermix of these two approaches and believe that hybrid models can better capture the mechanisms of the human mind (Sun and Bookman 1994).

See also

References

  1. ^ Arbib, p.666
  2. ^ Monterola, C., Roxas, R.M., and Carreon-Monterola, S. (2008). Characterizing the Effect of Seating Arrangement on Classroom Learning Using Neural Networks. Complexity, 14(4), 26-33. ISSN 1076-2782.
  3. ^ Roger Bridgman's defence of neural networks

Further reading

  • Arbib, Michael A. (Ed.) (1995). The Handbook of Brain Theory and Neural Networks. 
  • Alspector, U.S. Patent 4,874,963 "Neuromorphic learning networks". October 17, 1989.
  • Agre, Philip E. (1997). Computation and Human Experience. Cambridge University Press. ISBN 0-521-38603-9. , p. 80
  • Yaneer Bar-Yam (2003). Dynamics of Complex Systems, Chapter 2. 
  • Yaneer Bar-Yam (2003). Dynamics of Complex Systems, Chapter 3. 
  • Yaneer Bar-Yam (2005). Making Things Work.  See chapter 3.
  • Bertsekas, Dimitri P. (1999). Nonlinear Programming. 
  • Bertsekas, Dimitri P. & Tsitsiklis, John N. (1996). Neuro-dynamic Programming. 
  • Bhadeshia H. K. D. H. (1992). "Neural Networks in Materials Science". ISIJ International 39: 966–979. doi:10.2355/isijinternational.39.966. 
  • Boyd, Stephen & Vandenberghe, Lieven (2004). Convex Optimization. 
  • Dewdney, A. K. (1997). Yes, We Have No Neutrons: An Eye-Opening Tour through the Twists and Turns of Bad Science. Wiley, 192 pp.  See chapter 5.
  • Egmont-Petersen, M., de Ridder, D., Handels, H. (2002). "Image processing with neural networks - a review". Pattern Recognition 35 (10): 2279–2301. doi:10.1016/S0031-3203(01)00178-9. 
  • Fukushima, K. (1975). "Cognitron: A Self-Organizing Multilayered Neural Network". Biological Cybernetics 20: 121–136. doi:10.1007/BF00342633. 
  • Frank, Michael J. (2005). "Dynamic Dopamine Modulation in the Basal Ganglia: A Neurocomputational Account of Cognitive Deficits in Medicated and Non-medicated Parkinsonism". Journal of Cognitive Neuroscience 17: 51–72. doi:10.1162/0898929052880093. 
  • Gardner, E.J., & Derrida, B. (1988). "Optimal storage properties of neural network models". Journal of Physics a 21: 271–284. doi:10.1088/0305-4470/21/1/031. 
  • Krauth, W., & Mezard, M. (1989). "Storage capacity of memory with binary couplings". Journal de Physique 50: 3057–3066. doi:10.1051/jphys:0198900500200305700. 
  • Maass, W., & Markram, H. (2002). "On the computational power of recurrent circuits of spiking neurons". Journal of Computer and System Sciences 69(4): 593–616. 
  • MacKay, David (2003). Information Theory, Inference, and Learning Algorithms. 
  • Mandic, D. & Chambers, J. (2001). Recurrent Neural Networks for Prediction: Architectures, Learning algorithms and Stability. Wiley. 
  • Minsky, M. & Papert, S. (1969). An Introduction to Computational Geometry. MIT Press. 
  • Muller, P. & Insua, D.R. (1995). "Issues in Bayesian Analysis of Neural Network Models". Neural Computation 10: 571–592. 
  • Reilly, D.L., Cooper, L.N. & Elbaum, C. (1982). "A Neural Model for Category Learning". Biological Cybernetics 45: 35–41. doi:10.1007/BF00387211. 
  • Rosenblatt, F. (1962). Principles of Neurodynamics. Spartan Books. 
  • Sun, R. & Bookman,L. (eds.) (1994.). Computational Architectures Integrating Neural and Symbolic Processes.. Kluwer Academic Publishers, Needham, MA.. 
  • Sutton, Richard S. & Barto, Andrew G. (1998). Reinforcement Learning : An introduction. 
  • Van den Bergh, F. Engelbrecht, AP. Cooperative Learning in Neural Networks using Particle Swarm Optimizers. CIRG 2000. 
  • Wilkes, A.L. & Wade, N.J. (1997). "Bain on Neural Networks". Brain and Cognition 33: 295–305. doi:10.1006/brcg.1997.0869. 
  • Wasserman, P.D. (1989). Neural computing theory and practice. Van Nostrand Reinhold. 
  • Jeffrey T. Spooner, Manfredi Maggiore, Raul Ord onez, and Kevin M. Passino, Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques, John Wiley and Sons, NY, 2002.
  • http://www.cs.stir.ac.uk/courses/31YF/Notes/Notes_PL.html
  • http://www.shef.ac.uk/psychology/gurney/notes/l1/section3_3.html
  • Peter Dayan, L.F. Abbott. Theoretical Neuroscience. MIT Press. 
  • Wulfram Gerstner, Werner Kistler. Spiking Neuron Models:Single Neurons, Populations, Plasticity. Cambridge University Press. 
  • Steeb, W-H (2008). The Nonlinear Workbook: Chaos, Fractals, Neural Networks, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs: 4th edition. World Scientific Publishing. ISBN 981-281-852-9. 

External links


 
 

Did you mean: neural network (in computers, electronics), Neural Networks (journal)


 

Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
Britannica Concise Encyclopedia. Britannica Concise Encyclopedia. © 2006 Encyclopædia Britannica, Inc. All rights reserved.  Read more
Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.  Read more
Modern Science. The Dictionary of Cultural Literacy, Second Edition, Revised and updated Edited by E.D. Hirsch, Jr., Joseph F. Kett, and James Trefil. Copyright © 1993 by Houghton Mifflin Company . All rights reserved.  Read more
Computer Desktop Encyclopedia. THIS COPYRIGHTED DEFINITION IS FOR PERSONAL USE ONLY.
All other reproduction is strictly prohibited without permission from the publisher.
© 1981-2009 Computer Language Company Inc.  All rights reserved.  Read more
Investment Dictionary. Copyright ©2000, Investopedia.com - Owned and Operated by Investopedia Inc. All rights reserved.  Read more
Accounting Dictionary. Dictionary of Accounting Terms. Copyright © 2005 by Barron's Educational Series, Inc. All rights reserved.  Read more
Geography Dictionary. A Dictionary of Geography. Copyright © Susan Mayhew 1992, 1997, 2004. All rights reserved.  Read more
Columbia Encyclopedia. The Columbia Electronic Encyclopedia, Sixth Edition Copyright © 2003, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/ Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Neural network" Read more