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Computer Science Department
IBM Almaden Research Center
Michigan State University
East Lansing, MI 48824
San Jose, CA 95120
Numerous advances have been made in developing intelligent" programs, some
of which have been inspired by biological neural networks. Researchers from variousscientic disciplines are designing articial neural networks (ANNs) to solve a varietyof problems in decision making, optimization, prediction, and control. Articial neuralnetworks can be viewed as parallel and distributed processing systems which consistof a huge number of simple and massively connected processors. There has been aresurgence of interest in the eld of ANNs in recent years. This article intends to serveas a tutorial for those readers with little or no knowledge about ANNs to enable themto understand the remaining articles of this special issue. We discuss the motivationsbehind developing ANNs, main issues of network architecture and learning process, andbasic network models. We also briey describe one of the most successful applicationsof ANNs, namely automatic character recognition.

1 IntroductionWhat are articial neural networks (ANNs)? Why is there so much excitement about
ANNs? What are the basic models used in designing ANNs? What tasks can ANNs
perform eciently? These are the main questions addressed in this tutorial article.

Let us rst consider the following classes of challenging problems of interest to computer
scientists and engineers.

Pattern classication: The task of pattern classication is to assign an input pattern
(e.g., speech waveform or handwritten symbol) represented by a feature vector to one of pre-
specied classes (Fig. 1(a)). Well-known applications of pattern classication are character
recognition, speech recognition, EEG waveform classication, blood cell classication, and
printed circuit board inspection.

Clustering/categorization: In clustering, also known as unsupervised pattern classi-
cation, there are no training data with known class labels. A clustering algorithm explores
the similarity between the patterns and places similar patterns in a cluster (see Fig. 1(b)).

Well-known clustering applications include data mining, data compression, and exploratory
data analysis.

Function approximation: Given a set of n labeled training patterns (input-output
pairs), (x ;y );(x ;y ); ;(xn;yn) , generated from an unknown function (x) (subject
to noise), the task of function approximation is to nd an estimate, say , of the unknown
function (Fig. 1(c)). Various engineering and scientic modeling problems require function
Prediction/forecasting: Given a set of n samples y(t );y(t ); ;y(tn) in a time
sequence, t ;t ; ;tn, the task is to predict the sample y(tn ) at some future time tn .

Prediction/forecasting has a signicant impact on decision making in business, science and
engineering. Stock market prediction and weather forecasting are typical applications of
prediction/forecasting techniques (see Fig. 1(d)).

Optimization: A wide variety of problems in mathematics, statistics, engineering, sci-
ence, medicine, and economics can be posed as optimization problems. The goal of an
optimization algorithm is to nd a solution satisfying a set of constraints such that an objec-
tive function is maximized or minimized. A classical optimization problem is the Traveling
Salesperson Problem (TSP), which is an NP-complete problem.

Content-addressable memory: In the Von Neumann model of computation, an entry
in memory is accessed only through its address which is independent of the content in the
memory. Moreover, if a small error is made in calculating the address, a completely dierent
item would be retrieved. Associative memory or content-addressable memory, as the name
implies, can be accessed by its content. The content in the memory can be recalled even by a
partial input or distorted content (see Fig. 1(f)). Associative memory is extremely desirable
in building multimedia information databases.

Control: Consider a dynamic system dened by a tuple u(t);y(t) , where u(t) is the
control input and y(t) is the resulting output of the system at time t. In model-referenceadaptive control, the goal is to generate a control input u(t) such that the system follows
a desired trajectory determined by the reference model. An example of model reference
adaptive control is the engine idle speed control (Fig. 1(g)).

A large number of approaches have been proposed for solving the problems described
above. While successful applications of these approaches can be found in certain well-
constrained environments, none of them is exible enough to perform well outside the domain
for which it is designed. The eld of articial neural networks has provided alternative ap-
proaches for solving these problems. It has been established [1, 8, 6] that a large number of
applications can benet from the use of ANNs.

Articial neural networks, which are also referred to as neural computation, network
computation, connectionist models, and parallel distributed processing (PDP), are massively
parallel computing systems consisting of an extremely large number of simple processors
with many interconnections between them.

The purpose of this article is to serve as a tutorial for those readers with little or no
knowledge about articial neural networks. The rest of this article is organized as follows.

Section 2 provides the motivations behind developing ANNs. In Section 3, we describe the
basic neuron model, network architecture, and learning process. Sections 4 through 7 pro-
vide more details about several well-known ANN models: multilayer feedforward networks,
Kohonen's self-organizing maps, ART models and the Hopeld network. In Section 8, we
discuss character recognition, a popular and one of the most successful applications of ANN
models. Concluding remarks are presented in Section 9.

Pattern Classifier
over−fitting to
noisy training data
Airplane partially
Retrieved airplane
occluded by clouds
Figure 1: Tasks that neural networks can perform. (a) Pattern classication; (b)
clustering/categorization; (c) Function approximation; (d) Prediction/forecasting; (e)
Optimization (TSP problem); (f) Retrieval by content; and (g) Engine idle speed
2 MotivationANNs are inspired by biological neural networks. This section provides a brief introduction
to biological neural networks.

2.1 Biological Neural NetworksA neuron (or nerve cell) is a special biological cell with information processing ability. A
Figure 2: A sketch of a biological neuron.

schematic drawing of a neuron is shown in Fig. 2. A neuron is composed of a cell body,
or soma, and two types of out-reaching tree-like branches: axon and dendrites. The cell
body has a nucleus which contains information on hereditary traits and a plasma containing
molecular equipment for the production of material needed by the neuron. A neuron receives
signals (impulses) from other neurons through its dendrites (receivers), and transmits signals
generated by its cell body along the axon (transmitter) which eventually branches into
strands and substrands. At the terminals of these strands are the synapses. A synapse is
a place of contact between two neurons (an axon strand of one neuron and a dendrite of
another neuron). When the impulse reaches the synapse's terminal, certain chemicals, called
neurotransmitters are released. The neurotransmitters diuse across the synaptic gap, and
their eect is to either enhance or inhibit, depending on the type of the synapse, the receptor
neuron's own tendency to emit electrical impulses. The eectiveness of a synapse can be
adjusted by the signals passing through it so that the synapses can learn from the activities in
which they participate. This dependence on past history acts as a memory which is possibly
responsible for the human ability to remember.

The cerebral cortex in humans is a large at sheet of neurons about 2 to 3 mm thick with
a surface area of about 2,200 cm , about twice the area of a standard computer keyboard.

The cerebral cortex contains about 10 neurons, which is approximately the number of stars
in the Milky Way! Neurons are massively connected, much more complex and denser than
today's telephone networks. Each neuron is connected to 10 10 other neurons. In total,
the human brain contains approximately 10
Neurons communicate by a very short train of pulses, typically milliseconds in duration.

The message is modulated on the frequency with which the pulses are transmitted. The
frequency can vary from a few up to several hundred Hertz, which is a million times slower
than the fastest switching speed in electronic circuits. However, complex perceptual deci-
sions, such as face recognition, are made by a human very quickly, typically within a few
hundred milliseconds. These decisions are made by a network of neurons whose operational
speed is only a few milliseconds. This implies that computations involved cannot take more
than about one hundred serial stages. In other words, the brain runs parallel programs that
are about 100 steps long for such perceptual tasks. This is known as the hundred step rule
[5]. The same timing considerations show that the amount of information sent from one
neuron to another must be very small (a few bits). This implies that critical information
is not transmitted directly, but captured and distributed in the interconnections, and hence
the name connectionist model.

Interested readers can nd more introductory and easily comprehensible material on
biological neurons and neural networks in [3].

2.2 Why Articial Neural Networks?Modern digital computers have outperformed humans in the domain of numeric computation
and related symbol manipulation. However, humans can eortlessly solve complexperceptual
problems (e.g., recognizing a person in a crowd from a mere glimpse of his face) at such a
high speed and extent as to dwarf the world's fastest computer. Why does there exist such a
remarkable dierence in their performance? The biological computer employs a completely
dierent architecture than the Von Neumann architecture (see Table 1). It is this dierence
that signicantly aects the type of functions each computational model is best able to
Von Neumann computer
Biological computer
separate from a processor integrated into processor
non-content addressable
content addressable
numerical and symbolic
perceptual problems
Table 1: Von Neumann computer versus biological computer.

Numerous eorts have been made to develop intelligent" programs based on Von Neu-
mann's centralized architecture. However, such eorts have not resulted in any general-
purpose intelligent programs. ANN models are inspired by biological evidence, and attempt
to make use of some of the organizational" principles that are believed to be used in the
human brain. Our ability to model a biological nervous system using ANNs can increase our
understanding of biological functions. The state-of-the-art in computer hardware technology
(e.g., VLSI and optical) has made such modeling feasible.

The long course of evolution has resulted in the human brain possessing many desirable
characteristics which are neither present in a Von Neumann computer nor in modern paral-
lel computers. These characteristics include massive parallelism, distributed representation
and computation, learning ability, generalization ability, adaptivity, inherent contextual in-
formation processing, fault tolerance, and low energy consumption. It is hoped that ANNs,
motivated from biological neural networks, would possess some of these desirable character-
The eld of articial neural networks is an interdisciplinary area of research. A thorough
study of articial neural networks requires a knowledge about neurophysiology, cognitive sci-
ence/psychology, physics (statistical mechanics), control theory, computer science, articial
intelligence, statistics/mathematics, pattern recognition, computer vision, parallel process-
ing, and hardware (digital/analog/VLSI/optical). New developments in these disciplines
continuously nourish the eld of ANNs. On the other hand, articial neural networks also
provide an impetus to these disciplines in the form of new tools and representations. This
symbiosis is necessary for the vitality of neural network research. Communications among
these disciplines ought to be encouraged.

2.3 Brief Historical ReviewResearch in ANNs has experienced three consecutive cycles of enthusiasm and skepticism.

The rst peak, dating back to the 1940's, is due to McCullough and Pitt's pioneering work
[14]. The second period of intense activity occurred in the 1960's which featured Rosenblatt's
perceptron convergence theorem [18] and Minsky and Papert's work showing the limitations
of a simple perceptron [16]. Minsky and Papert's results dampened the enthusiasm of most
researchers, especially those in the computer science community. As a result, there was a
lull in the neural network research for almost 20 years. Since the early 1980's, ANNs have
received considerable renewed interest. The major developments behind this resurgence
include Hopeld's energy approach [9] in 1982, and the backpropagation learning algorithm
for multilayer perceptrons (multilayer feedforward networks) which was rst proposed by
Werbos [20], reinvented several times, and popularized by Rumelhart et al. [19] in 1986.

Anderson and Rosenfeld [2] provide a detailed historical account of developments in ANNs.

3 Articial Neural NetworksThis section provides an overview of ANNs. First, computational models of neurons are
introduced. Then, the important issues of network architecture and learning are discussed.

Various ANN models are organized by their architecture and the learning algorithm involved.

3.1 Computational Models of NeuronsMcCulloch and Pitts [14] proposed a binary threshold unit as a computational model for
a neuron. A schematic diagram of a McCulloch-Pitts neuron is shown in Fig. 3. This
Figure 3: McCulloch-Pitts model of a neuron.

mathematical neuron computes a weighted sum of its n input signals, xj; j = 1;2; ;n,
and generates an output of 1" if this sum is above a certain threshold u, and an output of
0" otherwise. Mathematically,
where ( ) is a unit step function at zero, and wj is the synapse weight associated with
the jth input. For simplicity of notation, we often consider the threshold u as another
weight w = u which is attached to the neuron with a constant input, x = 1. Positive
weights correspond to excitatory synapses, while negative weights model inhibitory synapses.

McCulloch and Pitts proved that with suitably chosen weights a synchronous arrangement of
such neurons is, in principle, capable of universal computation. There is a crude analogy here
to a biological neuron: wires and interconnections model axons and dendrites, connection
weights represent synapses, and the threshold function approximates the activity in soma.

The model of McCulloch and Pitts contains a number of simplifying assumptions, which do
not reect the true behavior of biological neurons.

The McCulloch-Pitts neuron has been generalized in many ways. An obvious generaliza-
tion is to use activation functions other than the threshold function, e.g., a piecewise linear,sigmoid, or Gaussian, shown in Fig. 4. The sigmoid function is by far the most frequently
used function in ANNs. It is a strictly increasing function that exhibits smoothness and has
the desired asymptotic properties. The standard sigmoid function is the logistic function,
g(x) = 1=(1 + exp( x) ;
where is the slope parameter.

Figure 4: Dierent types of activation functions.

3.2 Network ArchitectureAn assembly of articial neurons is called an articial neural network. ANNs can be viewed
as weighted directed graphs in which nodes are articial neurons and directed edges (with
weights) are connections from the outputs of neurons to the inputs of neurons. Based on the
connection pattern (architecture), ANNs can be grouped into two major categories as shown
in Fig. 5: (i) feedforward networks in which no loop exists in the graph, and (ii) feedback
(or recurrent) networks in which loops exist because of feedback connections. The most
common family of feedforward networks is a layered network in which neurons are organized
into layers with connections strictly in one direction from one layer to another. Fig. 5 also
shows typical networks of each category. We will discuss in this article all these networks
except for the Radial Basis Function (RBF) networks [6] which employ the same network
architecture as multilayer perceptrons, but dierent activation functions.

Dierent connectivities yield dierent network behaviors. Generally speaking, feedfor-
ward networks are static networks, i.e., given an input, they produce only one set of output
Feedforward Networks
Figure 5: A taxonomy of network architectures.

values, not a sequence of values. Feedforward networks are memoryless in the sense that the
response of a feedforward network to an input is independent of the previous state of the
network. Recurrent networks are dynamic systems. Upon presenting a new input pattern,
the outputs of the neurons are computed. Because of the feedback paths, the inputs to each
neuron are then modied, which leads the network to enter a new state.

Dierent network architectures require dierent learning algorithms. The next section
will provide a general overview of the various learning processes.

3.3 LearningThe ability to learn is a fundamental trait of intelligence. Although a precise denition of
learning is often dicult to state, a learning process in the context of articial neural networks
can be viewed as the problem of updating network architecture and connection weights
so that a network can eciently perform a specic task. Most of the time, the network
must learn the connection weights from the available training patterns. Improvement in
performance is achieved over time through iteratively updating the weights in the network.

The ability of articial neural networks to automatically learn from examples makes them
very attractive and exciting. Instead of having to specify a set of rules, ANNs appear to
learn them from the given collection of representative examples. This is one of the major
advantages of neural networks over traditional expert systems.

In order to understand or design a learning process, one must rst have a model of
the environment in which a neural network operates, i.e., what information is available to
the neural network. We refer to this model as a learning paradigm [6]. Second, one must
understand how weights in the network are updated, i.e., what are the learning rules which
govern the updating process. A learning algorithm refers to a procedure in which learning
rules are used for adjusting weights in the network.

There are three main learning paradigms, namely, (i) supervised, (ii) unsupervised, and
(iii) hybrid learning. In supervised learning or learning with a teacher, the network is provided
with a correct answer to every input pattern. Weights are determinedso that the network can
produce answers as close as possible to the known correct answers. Reinforcement learning
is a variant of supervised learning where the network is provided with only a critique on the
correctness of network outputs, not the correct answers (outputs) themselves. In contrast,unsupervised learning or learning without a teacher does not require any correct answer
associated with each input pattern in the training data set. It explores the underlying
structure in the data, or correlations between patterns in the data, and organizes patterns
into categories from these correlations. Hybrid learning combines supervised learning and
unsupervised learning. Typically, a portion of weights in the network are determined using
supervised learning, while the others are obtained from unsupervised learning.

Learning theory must address three fundamental and practical issues associated with
learning from samples: (i) capacity, (ii) sample complexity, and (iii) time complexity. Capac-ity concerns how many patterns can be stored, and what functions and decision boundaries
can be formed by a network.

Sample complexity determines the number of training patterns needed to train the net-
work in order to guarantee a valid generalization. Too few patterns may cause over-tting"
(wherein the network performs well on the training data set, but poorly on independent test
patterns drawn from the same distribution as the training patterns) (see Fig. 1(c)).

Computational complexity refers to the time requirement for a learning algorithm to
estimate a solution from the training patterns. Many existing learning algorithms have high
computational complexity. Designing ecient algorithms for neural network learning is a
very active research topic.

There are four basic types of learning rules: (i) error-correction, (ii) Boltzmann, (iii)
Hebbian, and (iv) competitive learning.

3.3.1 Error-Correction RulesIn the supervised learning paradigm, the network is given a desired output for each input
pattern. During the learning process, the actual output, y, generated by the network may
not equal the desired output, d. The basic principle of error-correction learning rules is to
use the error signal (d y) to modify the connection weights such that this error will be
gradually reduced.

The well-known perceptron learning rule is based on this error-correction principle. A
perceptron consists of a single neuron with adjustable weights, wj; j = 1;2; ;n, and
threshold , as shown in Fig. 3. Given an input vector x = (x ;x ; ;xn)t, the net input
to the neuron (before applying the threshold function) is
The output y of the perceptron is +1 if v > 0, and 0 otherwise. In a two-class classication
problem, the perceptron assigns an input pattern to one class if y = 1, and to the other class
if y = 0. The linear equation
denes the decision boundary (a hyperplane in the n-dimensional input space) which divides
the space into two halves.

Rosenblatt [18] developed a learning procedure to determine the weights and threshold
in a perceptron, given a set of training patterns. The perceptron learning procedure can be
described as follows.

1. Initialize the weights and threshold to small random numbers.

2. Present a pattern vector (x ;x ; ;xn)t, and evaluate the output of the neuron.

3. Update the weights according to
wj(t + 1) = wj(t) + (d y)xj;
where d is the desired output, t is iteration number, and (0:0 < < 1:0) is
the gain (step size).

Note that learning occurs only when an error is made by the perceptron. Rosenblatt
proved that if the training patterns are drawn from two linearly-separable classes, then
the perceptron learning procedure will converge after a nite number of iterations. This is
the well known perceptron convergence theorem. In practice, one does not know whether
the patterns are linearly separable or not. Many variations of this learning algorithm have
been proposed in the literature [8]. Other activation functions can also be used, which lead
to dierent learning characteristics. However, a single layer perceptron can only separatelinearly separable patterns, as long as a monotonic activation function is used.

The well-known backpropagation learning algorithm (described in section 4) is also based
on the error-correction principle.

3.3.2 Boltzmann LearningBoltzmann machines are symmetric recurrent networks consisting of binary units (+1 for
on" and -1 for o"). By symmetric, we mean that the weight on the connection from unit
i to unit j is equal to the weight on the connection from unit j to unit i (wij = wji). Only
a portion of neurons, visible neurons, interact with the environment, the rest, called hidden
neurons, do not interact. Each neuron is a stochastic unit which generates an output (or
state) according to the Boltzmann distribution of statistical mechanics. Boltzmann machines
operate in two modes: (i) Clamped mode in which visible neurons are clamped onto specic
states determined by the environment; and (ii) Free-running mode in which both the visible
and hidden neurons are allowed to operate freely.

Boltzmann learning is a stochastic learning rule derived from information-theoretic and
thermodynamic principles (see [2]). The objective of Boltzmann learning is to adjust the
connection weights such that the states of visible units satisfy a particular desired probability
distribution. According to the Boltzmann learning rule, the change in the connection weight
wij = (ij ij);
where is the learning rate, and ij and ij are the correlations between the states of
unit i and unit j when the network operates in the clamped mode and free-running mode,
respectively. The values of ij and ij are usually estimated from Monte Carlo experiments
which are extremely slow.

Boltzmann learning can be viewed as a special case of error-correction learning in which
error is measured not as the direct dierence between the desired output and actual output,
but as the dierence between the correlations between the outputs of two neurons under two
operating conditions (clamped and free-running).

3.3.3 Hebbian RuleThe oldest learning rule is Hebb's postulate of learning [7]. It was proposed by Hebb based
on the following observation from neurobiological experiments: if neurons on both sides of
a synapse are activated synchronously and repeatedly, then the strength of that synapse is
selectively increased [6].

Mathematically, the Hebbian rule can be described as
wij(t + 1) = wij(t) + yj(t)xi(t);
where xi and yj are the output values of neurons i and j, respectively, which are connected
by the synapse wij, and is the learning rate. Note that xi is the input to the synapse.

An important property of this rule is that learning is done locally, i.e., the change of
the synapse weight depends only on the activities of the two neurons connected by it. This
signicantly simplies the complexity of the learning circuit in a VLSI implementation.

A single neuron trained using the Hebbian rule exhibits an orientation selectivity. Fig. 6
demonstrates this property. The points depicted in Fig. 6 are drawn from a 2-dimensional
Gaussian distribution and used for training a neuron. The weight vector of the neuron is
initialized to w as shown in the gure. As the learning proceeds, the weight vector moves
closer and closer to the direction w of maximal variance in the data. In fact, w is the
eigenvector of the covariance matrix of the data corresponding to the largest eigenvalue.

Figure 6: Orientation selectivity of a single neuron trained using the Hebbian rule.

3.3.4 Competitive Learning RulesUnlike Hebbian learning (where multiple output units can be red simultaneously), compet-
itive learning has all the output units compete among themselves for activation. As a result
of such a competition, only one output unit, is active at any given time. This phenomenon
is often known as winner-take-all. Competitive learning has been found to exist in biological
neural networks [6].

The outcome of competitive learning is often a clustering or categorization of the input
data. Similar patterns are grouped by the network and represented by a single unit. This
grouping process is done by the network automatically based on the correlations in the data.

The simplest competitive learning network consists of a single layer of output units as
shown in Fig. 5. Each output unit i in the network connects to all the input units (xi's)
via weights, wij, j = 1;2; ;d. Each output unit also connects to all the other output
units via inhibitory weights, but has a self-feedback with an excitatory weight. As a result
of competition, only the unit i with the largest (or the smallest) net input becomes the
winner, i.e., wi x wi x; i; or wi x
wi x ; i: When all the weight vectors
are normalized, these two inequalities are equivalent.

A simple competitive learning rule can be stated as follows.

Note that only the weights of the winner unit get updated. The eect of this learning
rule is to move the stored pattern in the winner unit (weights) a little bit closer to the
input pattern. A geometric interpretation of competitive learning is demonstrated in Fig. 7.

In this example, we assume that all the input vectors have been normalized to have unit
length. They are depicted as black dots in Fig. 7(a). The weight vectors of the three
units are randomly initialized. Their initial positions and nal positions on the sphere after
competitive learning are shown as crosses in Figs. 7(a) and 7(b), respectively. As we can see
from Fig. 7, each of the three natural groups (clusters) of patterns has been discovered by
an output unit whose weight vector points to the center of gravity of the discovered group.

Figure 7: An example of competitive learning: (a) before learning; (b) after learning.

One can see from the competitive learning rule that the network will never stop learning
(updating weights) unless the learning rate is zero. It is possible that a particular input
pattern may re dierent output units at dierent iterations during learning. This brings up
the stability issue of a learning system. A learning system is said to be stable if no pattern
in the training data changes its category after a nite number of learning iterations. One
way of achieving stability is to force the learning rate to decrease gradually as the learning
process proceeds, and so it eventually approaches zero. However, this articial freezing of
learning causes another problem termed plasticity, which is dened as the ability to adapt to
new data. This is known as Grossberg's stability-plasticity dilemma in competitive learning.

The most well-known example of competitive learning is vector quantization for data
compression. Vector quantization has been widely used in speech and image processing for
ecient storage, transmission and modeling. The goal of vector quantization is to represent a
set or distribution of input vectors by a relatively small number of prototype vectors (weight
vectors), or a codebook. Once a codebook has been constructed and agreed upon, we need
only transmit or store the index of the corresponding prototype to the input vector. Given
an input vector, its corresponding prototype can be found through searching for the nearest
prototype in the codebook.

3.3.5 Summary of Learning AlgorithmsVarious learning algorithms and their associated network architectures are summarized in
Table 2. However, this is by no means an exhaustive list of the learning algorithms available
in the literature. Both supervised and unsupervised learning paradigms employ learning
rules based on error-correction, Hebbian, and competitive learning. Learning rules based on
error-correction can be used for training feedforward networks, while Hebbian learning rules
have been used for all types of network architectures. However, each learning algorithm
is designed for training a specic network architecture. Therefore, when we talk about a
learning algorithm, it is implied that there is a particular network architecture associated
with it. Each learning algorithm is able to perform well on at most a few tasks. The last
column of table 2 lists a number of tasks that each learning algorithm can perform. Due
to space limitations, we will not discuss some of the other algorithms, including ADALINE,
MADALINE [13], linear discriminant analysis [10], ART2, ARTMAP [4], Sammon's projec-
tion [10], and principal component analysis [8]. Interested readers can further consult the
corresponding references (in order to reduce the size of the bibliography, this article does
not always cite the rst paper that proposed a particular algorithm).

4 Multilayer Feedforward NetworksFig. 8 shows a typical 3-layer perceptron. In general, a standard L-layer feedforward network1
consists of one input stage, (L 1) hidden layers, and one output layer of units which are
successively connected (fully or locally) in a feedforward fashion with no connections between
units in the same layer and no feedback connections between layers.

The most popular class of multi-layer feedforward networks is multi-layer perceptrons in
Learning Algorithm
Perceptron learning algorithms
pattern classication
function approximation
ADALINE & MADALINE
prediction, control
Boltzmann learning algorithm
pattern classication
Linear discriminant analysis
pattern classication
Learning vector quantization
pattern classication
Sammon's projection
Principal component analysis
Associative memory learning
associative memory
Vector quantization
pattern classication
RBF learning algorithm
function approximation
prediction, control
Table 2: Well-known learning algorithms.

which each computational unit employs either the thresholding function or the sigmoid func-
tion. Multi-layer perceptrons are capable of forming arbitrarily complex decision boundaries
and can represent any Boolean function [16]. The development of the back-propagation learn-
ing algorithm for determining weights in a multi-layer perceptron has made these networks
the most popular among researchers as well as users of neural networks.

We denote wij l as the weight on connection between the ith unit in layer (l 1) to jth
unit in layer l.

Let (x ;d );(x ;d ); ;(x p ;d p ) be a set of p training patterns (input-output
pairs), where x i Rn is the input vector in the n-dimensional pattern space, and d i
[0;1]m, a m-dimensional hyper-cube. For classication purposes, m is the number of classes.

The squared-error cost function, which is most frequently used in the ANN literature, is
The back-propagation algorithm [19] is a gradient-descent method to minimizethe squared-
Figure 8: A typical 3-layer feedforward network architecture.

error cost function in Equation (2), and is given below.

1. Initialize the weights to small random values;
2. Randomly choose an input pattern x ;
3. Propagate the signal forward through the network;
4. Compute Li in the output layer (oi = yLi)
where hli represents the net input to the ith unit in the lth layer, and g is the
derivative of the activation function g.

5. Compute the deltas for the preceding layers by propagating the errors back-
for l = (L 1); ;1.

6. Update weights using
7. Go to step 2 and repeat for the next pattern until the error in the output layer is
below a pre-specied threshold or a maximum number of iterations is reached.

A geometric interpretation (adopted and modied from [13]) shown in Fig. 9 can help
explicate the role of hidden units (with the threshold activation function). Each unit in
the rst hidden layer forms a hyper-plane in the pattern space; boundaries between pattern
classes can be approximated by hyper-planes. A unit in the second hidden layer forms a
hyper-region from the outputs of the rst-layer units; a decision region is obtained by per-
forming an AND" operation on hyperplanes. The output-layer units combine the decision
regions made by the units in the second hidden layer by performing logical OR" operations.

Remember that this scenario is depicted only to help us understand the role of hidden units.

Their actual behavior, after we train the network, could be dierent from this. A two-layer
network can form more complex decision boundaries than what is depicted in Fig. 9. More-
over, multilayer perceptrons with sigmoid activation functions can form smooth decision
boundaries rather than piece-wise linear boundaries.

Figure 9: A geometric interpretation of the role of hidden units.

A special class of multi-layer feedforward networks is the Radial Basis Function (RBF)
network [6], a two-layer network. Each unit in the hidden layer employs a radial basis
function, such as a Gaussian kernel, as the activation function. The radial basis function (or
kernel function) is centered at the point specied by the weight vector, associated with the
unit. Both the positions and the widths of these kernels must be learned from the training
patterns. The number of kernels in the RBF network is usually much less than the number
of training patterns. Each output unit implements a linear combination of these radial basis
functions. From the point of view of function approximation, the hidden units provide a set
of functions that constitute an arbitrary basis" for representing input patterns in the space
spanned by the hidden units.

There are a variety of learning algorithms for the RBF network [6]. The basic algorithm
employs a two-step learning strategy (hybrid learning): estimation of kernel positions and
kernel widths using some unsupervised clustering algorithm, followed by a supervised least
mean square (LMS) type of algorithm to determine the connection weights to the output
layer. Since the output units are linear, a non-iterative algorithm can be used. After this
initial solution is obtained, a supervised gradient-based algorithm can be used to rene the
network parameters.

This hybrid learning algorithm for training the RBF network converges much faster than
the backpropagation algorithm for training multi-layer perceptrons. However, for many
problems, the RBF network often involves a larger number of hidden units compared with
a multi-layer perceptron. This implies that the run-time (after training) speed of the RBF
network is often slower than the run-time speed of a multi-layer perceptron. The eciencies
(error versus network size) of the RBF network and the multi-layer perceptron are, however,
problem-dependent. It has been shown that the RBF network has the same asymptotic
approximation power as a multi-layer perceptron.

There are many issues in designing feedforward networks. These issues include: (i) how
many layers are needed for a given task?; (ii) how many units per layer?; (iii) what can
we expect a network to generalize on data not included in the training set?; and (iv) how
large should the training set be for good" generalization? Although multilayer feedforward
networks using backpropagation have been widely used for classication and function ap-
proximation (see [8]), many design parameters still have to be determined by trial-and-error.

Existing theoretical results provide only very loose guidelines for selecting these parameters
in practice.

5 Kohonen's Self-Organizing MapsKohonen's self-organizing map (SOM) [11] has the desirable property of topology preser-
vation which captures an important aspect of the feature maps in the cortex of the more
developed animal brains. By a topology preserving mapping, we mean that nearby input
patterns should activate nearby output units on the map. The basic network architecture
of Kohonen's SOM is shown in Fig. 5. It basically consists of a two-dimensional array of
units, each of which is connected to all d input nodes. Let wij denote the d-dimensional
vector associated with the unit at location (i;j) of the 2-D array. Each neuron computes
the Euclidean distance between the input vector x and the stored weight vector wij.

Kohonen's SOM is a special type of competitive learning network which denes a spatial
neighborhood for each output unit. The shape of the local neighborhood can be either square,
rectangular, or circular. Initial neighborhood size is often set to 1/2 to 2/3 of the network
size, and shrinks with time according to some schedule (e.g., an exponentially decreasing
function). During competitive learning, all the weight vectors associated with the winner
and its neighboring units are updated.

Kohonen's SOM learning algorithm can be described as follows.

1. Initialize weights to small random numbers; set initial learning rate and neigh-
2. Present a pattern x, and evaluate the network outputs;
3. Select the unit (ci;cj) with the minimum output:
4. Update all the weights
according to the following learning rule;
ij(t) + (t)[x(t)
ij(t)]; if (i; j)
where Nc c (t) is the neighborhood of the unit (ci;cj) at time t, and (t) is the
learning rate.

5. Decrease the value of (t) and shrink the neighborhood Nc c (t);
6. Repeat steps 2 { 5 until the change in weight values is less than a pre-specied
threshold, or a maximum number of iterations is reached.

Kohonen's SOM can be used for projection of multivariate data, density approximation,
and clustering. Some successful applications of Kohonen's SOM can be found in the areas of
speech recognition, image processing, robotics, and process control [8]. The design param-
eters include the dimensionality of the neuron array, number of neurons in each dimension,
shape of neighborhood, shrinking schedule of the neighborhood, and the learning rate.

6 Adaptive Resonance Theory ModelsRecall that an important issue in competitive learning is the stability-plasticity dilemma.

How do we learn new things (plasticity) and yet retain the stability which ensures that
the existing knowledge is not erased or corrupted? Carpenter and Grossberg's Adaptive
Resonance Theory models (ART1, ART2, and ARTMAP) were developed in an attempt to
overcome this dilemma [4]. The basic idea of these models is as follows. The network has a
sucient supply of output units, but they are not used until deemed necessary. A unit is said
to be committed (uncommitted) if it is (is not) being used. The learning algorithm updates
the stored prototypes of a category only if the input vector is suciently similar to them. An
input vector and a stored prototype are said to resonate when they are suciently similar.

The extent of similarity is controlled by a vigilance parameter, , with 0 < < 1, which also
determines the number of categories. When the input vector is not suciently similar to
any existing prototype in the network, a new category is created and an uncommitted unit
is assigned to this new category with the input vector as the initial prototype. If no such
uncommitted unit exists, then a novel input generates no response.

Competitive (output) Layer
Comparison (input) Layer
Figure 10: ART1 network.

We present only ART1 which takes binary (0/1) input to illustrate the model. Fig. 10
shows a simplied diagram of the ART1 architecture (see [8]). It consists of two layers of
units which are fully connected. A top-down weight vector wj is associated with unit j in
the input layer, and bottom-up weight vector wi is associated with output unit i; wi is the
normalized version of wi.

where " is a small number which is used to break the ties in selecting the winner. The
top-down weight vectors, wj's, store the prototypes of clusters. The role of normalization
is to prevent prototypes with a long vector length from dominating prototypes with a short
vector length. Given an N-bit input vector x, the output of the auxiliary unit A is given by
A = Sgn = (Xxj N XOi 0:5);
where Sgn = (x) is the signum function which produces +1 if x 0 and 0 otherwise, and
the output of an input unit is given by
Vj = Sgn = (xj + XwjiOi + A 1:5)
if no output Oj is on";
i wjiOi; otherwise:
A reset signal R is generated only when the similarity is less than the vigilance level.

The ART1 learning algorithm is described below.

1. Initialize wij = 1, for all i;j. Enable all the output units.

2. Present a new pattern x.

3. Find the winner unit i among the enabled output units
4. Vigilance test
If r (resonance), goto Step 5. Otherwise, disable unit i and goto Step 3
(until all the output units are disabled).

5. Update the winning weight vector wi , enable all the output units and goto
wji = (Vj wji ):
6. If all the output units are disabled, select one of the uncommitted output units
and set its weight vector to x. If there is no uncommitted output unit (capacity
is reached), the network rejects the input pattern.

The ART1 model is able to create new categories and to reject an input pattern when
the network reaches its capacity. However, the number of categories discovered in the input
data by ART1 is sensitive to the vigilance parameter.

7 Hopeld NetworkThe Hopeld network uses a network energy function as a tool for designing recurrent net-
works and for understanding its dynamic behavior [9]. Hopeld's formulation made explicit
the principle of storing information as dynamically stable attractors, and popularized the
use of recurrent networks for associative memory and for solving combinatorial optimization
A Hopeld network with N units has two versions: binary and continuous valued net-
works. Let vi be the state or output of the ith unit. For binary networks, vi is either +1
or -1, but for continuous networks, vi can be any value between 0 and 1. Let wij be the
synapse weight on the connection from unit i to unit j. In Hopeld network, wij = wji; i;j
(symmetric network), and wii = 0; i (no self-feedback connections). The network dynamics
for the binary Hopeld network is
vi = Sgn(Xwijvj i):
The dynamic update of network states in Equation (4) can be carried out in at least
two ways: synchronously and asynchronously. In a synchronous updating scheme, all the
units are updated simultaneously at each time step. A central clock is therefore required to
synchronize the process. On the other hand, an asynchronous updating scheme selects one
unit at a time, and updates its state. The unit for updating can be chosen randomly.

The energy function of the binary Hopeld network in a state v = (v ;v ; ;vN)T is
The central property of the energy function is that as the state of network evolves according
to the network dynamics (Eq. (4)), the network energy always decreases, and eventually
reaches a local minimum point (attractor) where the network stays with a constant energy.

Suppose a set of patterns is stored in these attractors of a network. Then it can be used
as an associative memory. Any pattern present in the basin of attraction of a stored pattern
can be used as an index to retrieve it.

An associative memory usually operates in two phases: storage and retrieval. In the
storage phase, the weights in the network are determined in such a way that the attractors
of the network memorize a set of p N-dimensional patterns x ;x ; ;xp to be stored. A
generalization of the Hebbian learning rule can be used for setting connection weights wij.

In the retrieval phase, the input pattern is used as the initial state of the network, and the
network evolves according to the network dynamics. A pattern is produced (or retrieved)
when the network reaches an equilibrium state.

How many patterns can be stored in a network with N binary units? In other words,
what is the memory capacity of a network? Note that the capacity is nite because a network
with N binary units has a maximum of 2N distinct states, and not all of them are attractors.

Moreover, not all the attractors (stable states) can store useful patterns. There also existspurious attractors which store patterns dierent from any of the patterns in the training
It has been shown that the maximumnumber of random patterns that a Hopeld network
can store is Pmax 0:15N. If the number of stored patterns p < 0:15N, then a nearly
perfect recall can be achieved. If memory patterns are orthogonal vectors instead of random
patterns, then more patterns can be stored. But, the number of spurious attractors increases
as p reaches the capacity limit. Several learning rules have been proposed for increasing the
memory capacity of Hopeld networks (see [8]). Note that we require N connections in the
network to store p N-bit patterns.

Hopeld networks always evolve in the direction that leads to a lower network energy.

This implies that if a combinatorial optimization problem can be formulated as minimizing
the network energy, then the Hopeld network can be used to nd the optimal (or subopti-
mal) solution by letting the network evolve freely. In fact, any quadratic objective function
can be rewritten in the form of Hopeld network energy. For example, the classical traveling
salesperson problem can be formulated as a network energy minimization problem.

8 ApplicationsWe have discussed a number of important ANN models and learning algorithms proposed
in the literature. These ANN models and learning algorithms have been widely used for
solving the seven classes of problems that are described in Section 1. In Table 2, we show
the typical tasks that each of the ANN models and learning algorithms is particularly suitable
for. It is important to keep in mind that in order to successfully apply an ANN model and
learning algorithm to a real-world problem, one must deal with a number of design issues,
including network model, network size, activation function, learning parameters, and number
of trainign samples. In this section, we take one of the most successful applications of ANNs,Optical Character Recognition (OCR), as an example to illustrate how multilayer feedforward
networks are used in practice.

OCR deals with the problem of processing a scanned image of text and transcribing it
into a machine readable form. In this section we will outline the basic components of OCR
and explain how ANNs are used for character classication.

An OCR system usually consists of the following modules: (i) preprocessing, (ii) segmen-
tation, (iii) feature extraction, (iv) classication, and (v) contextual processing. A paper
document is scanned to produce a gray level or binary (black-and-white) image. In the
preprocessing stage, ltering is applied to remove noise, and text areas are located and con-
verted to a binary image using either a global or a local adaptive thresholding method. In
the segmentation step, the text image is separated into individual characters. This is a
particularly dicult task with handwritten text where there is a proliferation of touching
characters. One eective technique is to break the composite pattern into smaller patterns
(over-segmentation) and nd the correct character segmentation points using the output of
a pattern classier.

Recognizing segmented characters is not an easy task because there are many dierent
writing styles, dierent degrees of slant, skew, and noise level. This is evident from Fig. 11
which shows the size-normalized character bitmaps of a sample set from the NIST hand-print
character database [21].

There are two main schemes for using ANNs in an OCR system as shown in Fig. 12.

The rst scheme employs an explicit feature extractor (not necessarily a neural network).

Figure 11: A sample set of characters in the NIST data.

For instance, contour direction features are used in Fig. 12. The extracted features are
passed to the input stage of a multilayer feedforward network (e.g., [17]). This scheme
is very exible in incorporating a large variety of features. The other scheme does not
explicity extract features from the raw data. The feature extraction implicitly takes place
within the intermediate stages of the ANN. A nice property of this scheme is that feature
extraction and classication are integrated and trained simultaneously to produce optimal"
classication results. It is not clear whether the types of features which can be extracted by
this integrated architecture are the most eective ones for character recognition. Moreover,
this scheme requires a much larger network than the rst scheme.

A typicalexampleof this integrated feature extraction-classication schemeis the network
developed by Le Cun et al. [12] for zip-code recognition. A 16 16 normalized gray level
image is presented to a feedforward network with three hidden layers. The units in the rst
hidden layer are locally connected to the units in input layer, forming a set of local feature
maps. The second hidden layer is constructed in a similar way as the rst hidden layer.

Each unit in the second hidden layer also combines local information coming from feature
maps in the rst hidden layer. The activation level of an output unit can be interpreted
as an approximation of the a posteriori probability of belonging to a particular class given
the input pattern. The output categories are ordered according to activation levels and
passed to the post-processing stage. In the post-processing stage, contextual information is
Contour direction features
Recognizedtext in ASCII
Figure 12: Two schemes for using ANNs in an OCR system.

exploited to update the output of the classier. This could, for example, involve looking up
a dictionary of admissible words, or utilizing syntactic constraints present, for example, in
phone numbers or social security numbers.

How good are ANNs for OCR? ANNs are found to work very well in practice. However,
there is no conclusive evidence about ANN's superiority over conventional statistical pattern
classiers. At the First Census Optical Character Recognition System Conference held in
1992 [21], more than 40 dierent handwritten character recognition systems were evaluated
based on their performance on a common database. The top ten performers among them
used either some type of multilayerfeedforward network or a nearest neighbor-based classier.

ANNs tend to be superior in terms of speed and memory requirements compared to nearest
neighbor methods. Unlike the nearest neighbor methods, classication speed using ANNs
is independent of the size of the training set. The recognition accuracies of the top OCR
systems on the NIST isolated (pre-segmented) character data were above 98% for digits,
96% for upper-case characters, and 87% for lower-case characters. One conclusion drawn
from the test is that the recognition performance of OCR systems on isolated characters is
comparable to the human performance. However, humans still outperform OCR systems on
unconstrained and cursive handwritten documents.

9 Concluding RemarksDevelopments in ANNs have stimulated a lot of enthusiasm and criticism as well. Many
comparative studies provide an optimistic outlook for ANNs, while others oer a pessimistic
view. For many tasks, such as pattern recognition, no single approach dominates the other.

The choice of the best technique should be driven by the nature of the given application.

We should try to understand the capacities, assumptions, and applicability of various ap-
proaches, and maximally exploit the complementary advantages of these approaches in order
to develop better intelligent systems. Such an eort may lead to a synergistic approach which
combines the strengths of ANNs and other approaches in order to achieve a signicantly bet-
ter performance for challenging problems. As Minsky [15] has observed, the time has come
to build systems out of diverse components. In such a synergistic approach, not only are
individual modules important, but we also need a good methodology for integration. It is
clear that communication and cooperative work between researchers working in ANNs and
other disciplines will not only avoid repetitious work but, more importantly, will stimulate
and benet individual disciplines.

Acknowledgment: The authors would like to thank Richard Casey (IBM Almaden), Pat
Flynn (Washington State Univ.), William Punch, Chitra Dorai and Kalle Karu (Michigan
State Univ.), Ali Khotanzad (Southern Methodist Univ.), and Ishwar Sethi (Wayne State
Univ.) for their many useful suggestions.

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Source: http://metalab.uniten.edu.my/~abdrahim/ntl/jain96_NN_Tutorial.pdf

Original Article · Originalarbeit Forsch Komplementmed 2014;21:239–245 Published online: August 5, 2014 Evidence for the Efﬁcacy of a Bioresonance Method in Smoking Cessation: A Pilot Study Aylin Pihtilia Michael Galleb Caglar Cuhadarogluc Zeki Kilicaslana Halim Isseverd Feyza Erkana Tulin Cagataya Ziya Gulbarana a Department of Pulmonary Diseases, Faculty of Medicine, University of Istanbul, Turkeyb Institute for Biophysical Medicine, Idar-Oberstein, Germanyc Department of Pulmonary Diseases, Faculty of Medicine, Acibadem University, Istanbul, Turkeyd Department of Community Health, Faculty of Medicine, University of Istanbul, Turkey

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