Arti cial Neural Networks: A Tutorial 1 Introduction - Department of

33 Pages·1999·0.31 MB·English

Appeared in IEEE Computer, Vol.29, No.3. March, 1996. pp.31-44.
Arti(cid:12)cial Neural Networks: A Tutorial
(cid:3) + +
Anil K. Jain Jianchang Mao K. Mohiuddin
(cid:3) +
Computer Science Department IBM Almaden Research Center
Michigan State University 650 Harry Road
East Lansing, MI 48824 San Jose, CA 95120
Abstract
Numerous advances have been made in developing \intelligent" programs, some
of which have been inspired by biological neural networks. Researchers from various
scienti(cid:12)c disciplines are designing arti(cid:12)cial neural networks (ANNs) to solve a variety
of problems in decision making, optimization, prediction, and control. Arti(cid:12)cial neural
networks can be viewed as parallel and distributed processing systems which consist
of a huge number of simple and massively connected processors. There has been a
resurgence of interest in the (cid:12)eld of ANNs in recent years. This article intends to serve
as a tutorial for those readers with little or no knowledge about ANNs to enable them
to understand the remaining articles of this special issue. We discuss the motivations
behind developing ANNs,mainissuesofnetworkarchitectureandlearning process,and
basic network models. We also brie(cid:13)y describe one of the most successful applications
of ANNs, namely automatic character recognition.
1 Introduction
What are arti(cid:12)cial 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 e(cid:14)ciently? These are the main questions addressed in this tutorial article.
Let us (cid:12)rst consider the following classes of challenging problems of interest to computer
scientists and engineers.
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Pattern classi(cid:12)cation: The task of pattern classi(cid:12)cation is to assign an input pattern
(e.g., speech waveformor handwritten symbol) representedby a feature vector to one of pre-
speci(cid:12)ed classes (Fig. 1(a)). Well-known applications of pattern classi(cid:12)cation are character
recognition, speech recognition, EEG waveform classi(cid:12)cation, blood cell classi(cid:12)cation, and
printed circuit board inspection.
Clustering/categorization: In clustering, also known as unsupervised pattern classi-
(cid:12)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), f(x1;y1);(x2;y2);(cid:1)(cid:1)(cid:1);(xn;yn)g, generated from an unknown function (cid:22)(x) (subject
to noise), the task of function approximation is to (cid:12)nd an estimate, say (cid:22)^, of the unknown
function (cid:22) (Fig. 1(c)). Various engineeringand scienti(cid:12)cmodelingproblemsrequirefunction
approximation.
Prediction/forecasting: Given a set of n samples fy(t1);y(t2);(cid:1)(cid:1)(cid:1);y(tn)g in a time
sequence, t1;t2;(cid:1)(cid:1)(cid:1);tn, the task is to predict the sample y(tn+1) at some future time tn+1.
Prediction/forecasting has a signi(cid:12)cant 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
optimizationalgorithm is to (cid:12)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 smallerror is made in calculating the address, a completelydi(cid:11)erent
item would be retrieved. Associative memory or content-addressable memory, as the name
implies,can be accessed by its content. The contentin the memorycan be recalledevenby a
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partial input or distorted content (see Fig. 1(f)). Associative memoryis extremelydesirable
in building multimedia information databases.
Control: Consider a dynamic system de(cid:12)ned by a tuple fu(t);y(t)g, where u(t) is the
control input and y(t) is the resulting output of the system at time t. In model-reference
adaptive 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-
constrainedenvironments,noneofthemis(cid:13)exibleenough toperformwelloutsidethedomain
for which it is designed. The (cid:12)eld of arti(cid:12)cial 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 bene(cid:12)t from the use of ANNs.
Arti(cid:12)cial 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 arti(cid:12)cial 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 Hop(cid:12)eld 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.
3
Cardiogram Normal
Pattern Classifier
Abnormal
++++++++++++ +++++++++++ ++++++++++++++++++
(a) (b)
y Stock value
y
over−fitting to
noisy training data
?
true function
x t1 t2 t3 tn tn+1 t
(c) (d)
B
C
Airplane partially Retrieved airplane
occluded by clouds
E
Associative
A
Memory
D
(e) (f)
Load torque
Idle
speed
Throttle Engine
angle
Controller
(g)
Figure 1: Tasks that neural networks can perform. (a) Pattern classi(cid:12)cation; (b)
clustering/categorization; (c)Functionapproximation;(d)Prediction/forecasting;(e)
Optimization (TSP problem); (f) Retrieval by content; and (g) Engine idle speed
control.
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2 Motivation
ANNs are inspired by biological neural networks. This section provides a brief introduction
to biological neural networks.
2.1 Biological Neural Networks
A neuron (or nerve cell) is a special biological cell with information processing ability. A
Dendrites
Synapse
Axon
Cell body
Nucleus
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
molecularequipmentfor theproduction of materialneededby the neuron. A neuron receives
signals (impulses)fromother neurons through its dendrites(receivers),and transmitssignals
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 impulsereaches the synapse’s terminal,certain chemicals,called
neurotransmitters are released. The neurotransmitters di(cid:11)use across the synaptic gap, and
their e(cid:11)ectis to eitherenhance or inhibit,depending on the type of the synapse, the receptor
neuron’s own tendency to emit electrical impulses. The e(cid:11)ectiveness of a synapse can be
adjustedbythesignalspassing through itsothat thesynapses canlearnfromtheactivitiesin
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which they participate. This dependence on past history acts as a memorywhich is possibly
responsible for the human ability to remember.
The cerebral cortex in humans is a large (cid:13)at sheet of neurons about 2 to 3 mmthickwith
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a surface area of about 2,200 cm , about twice the area of a standard computer keyboard.
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The cerebral cortexcontains about 10 neurons, which is approximatelythe numberof stars
in the Milky Way! Neurons are massively connected, much more complex and denser than
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today’s telephone networks. Each neuron is connected to 10 (cid:0)10 other neurons. In total,
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the human brain contains approximately 10 (cid:0)10 interconnections.
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 (cid:12)nd more introductory and easily comprehensible material on
biological neurons and neural networks in [3].
2.2 Why Arti(cid:12)cial Neural Networks?
Modern digitalcomputershaveoutperformedhumansinthe domainof numericcomputation
andrelatedsymbolmanipulation. However,humanscane(cid:11)ortlesslysolvecomplexperceptual
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 di(cid:11)erence in their performance? The biological computer employs a completely
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di(cid:11)erent architecture than the Von Neumann architecture (see Table 1). It is this di(cid:11)erence
that signi(cid:12)cantly a(cid:11)ects the type of functions each computational model is best able to
perform.
Von Neumann computer Biological computer
complex simple
Processor high speed low speed
one or a few a large number
separate from a processor integrated into processor
Memory localized distributed
non-content addressable content addressable
centralized distributed
Computing sequential parallel
stored programs self-learning
Reliability very vulnerable robust
Expertise numerical and symbolic perceptual problems
manipulations
Operating well-de(cid:12)ned, poorly-de(cid:12)ned,
environment well-constrained unconstrained
Table 1: Von Neumann computer versus biological computer.
Numerous e(cid:11)orts have been made to develop \intelligent" programs based on Von Neu-
mann’s centralized architecture. However, such e(cid:11)orts 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 abilityto modela biological nervous system using ANNs can increase our
understanding of biological functions. The state-of-the-art in computerhardware 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-
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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-
istics.
The (cid:12)eld of arti(cid:12)cial neural networks is an interdisciplinaryarea of research. A thorough
study of arti(cid:12)cial neural networks requiresa knowledge about neurophysiology, cognitivesci-
ence/psychology, physics (statistical mechanics), control theory, computer science, arti(cid:12)cial
intelligence, statistics/mathematics, pattern recognition, computer vision, parallel process-
ing, and hardware (digital/analog/VLSI/optical). New developments in these disciplines
continuously nourish the (cid:12)eld of ANNs. On the other hand, arti(cid:12)cial 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 Review
Research in ANNs has experienced three consecutive cycles of enthusiasm and skepticism.
The (cid:12)rst peak, dating back to the 1940’s, is due to McCullough and Pitt’s pioneering work
[14]. Thesecond period ofintenseactivityoccurred inthe1960’s whichfeaturedRosenblatt’s
perceptron convergencetheorem [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 Hop(cid:12)eld’s energy approach [9] in 1982, and the backpropagation learning algorithm
for multilayer perceptrons (multilayer feedforward networks) which was (cid:12)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.
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3 Arti(cid:12)cial Neural Networks
This section provides an overview of ANNs. First, computational models of neurons are
introduced. Then, the important issues of network architecture and learning are discussed.
VariousANNmodelsareorganized bytheirarchitectureandthelearningalgorithminvolved.
3.1 Computational Models of Neurons
McCulloch 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
x1 w1
x2 w2 h y
wn u
xn
Figure 3: McCulloch-Pitts model of a neuron.
mathematical neuron computes a weighted sum of its n input signals, xj; j = 1;2;(cid:1)(cid:1)(cid:1);n,
and generates an output of \1" if this sum is above a certain threshold u, and an output of
\0" otherwise. Mathematically,
n
0 1
y = (cid:18) wjxj (cid:0)u ;
X
@j=1 A
where (cid:18)((cid:1)) is a unit step function at zero, and wj is the synapse weight associated with
th
the j input. For simplicity of notation, we often consider the threshold u as another
weight w0 = (cid:0)u which is attached to the neuron with a constant input, x0 = 1. Positive
weights correspond to excitatory synapses, whilenegative weights modelinhibitory synapses.
McCullochand Pitts provedthat with suitablychosen weightsa synchronous arrangementof
suchneurons is, inprinciple,capableof universalcomputation. Thereis acrudeanalogy 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 re(cid:13)ect the true behavior of biological neurons.
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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,
de(cid:12)ned by
g(x) = 1=(1+exp((cid:0)(cid:12)x));
where (cid:12) is the slope parameter.
Threshold Piecewise linear Sigmoid Gaussian
Figure 4: Di(cid:11)erent types of activation functions.
3.2 Network Architecture
An assembly of arti(cid:12)cial neurons is called an arti(cid:12)cial neural network. ANNs can be viewed
as weighted directed graphs in which nodes are arti(cid:12)cial 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
commonfamily 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 di(cid:11)erent activation functions.
Di(cid:11)erent connectivities yield di(cid:11)erent network behaviors. Generally speaking, feedfor-
ward networks are static networks, i.e., given an input, they produce only one set of output
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