Neural Networks_ Lecture Notes

8/11/2019 Neural Networks_ Lecture Notes

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NEURAL NETWORKSby Christos Stergiou and Dimitrios Siganos

Abstract

This report is an introduction to Artificial Neural Networks. The various types of neural networks

are explained and demonstrated applications of neural networks like ANNs in medicine are

described and a detailed historical background is provided. The connection between the artificialand the real thing is also investigated and explained. !inally the mathematical models involved arepresented and demonstrated.

Contents:

1. Introduction to Neural Networs

1.1 W!at is a neural networ"

1.# $istorical bac%round

1.& W!' use neural networs"

1.( Neural networs )ersus con)entional co*+uters , a co*+arison

#. $u*an and Arti-icial Neurones , in)esti%atin% t!e si*ilarities

#.1 $ow t!e $u*an rain Learns"

#.# /ro* $u*an Neurones to Arti-icial Neurones

&. An En%ineerin% a++roac!

&.1 A si*+le neuron , descri+tion o- a si*+le neuron

&.# /irin% rules , $ow neurones *ae decisions

&.& 0attern reco%nition , an ea*+le

&.( A *ore co*+licated neuron

(. Arc!itecture o- neural networs

(.1 /eed,-orward 2associati)e3 networs(.# /eedbac 2autoassociati)e3 networs

(.& Networ la'ers

(.( 0erce+trons

4. T!e Learnin% 0rocess

4.1 Trans-er /unction

4.# An Ea*+le to illustrate t!e abo)e teac!in% +rocedure

4.& T!e ac,0ro+a%ation Al%orit!*

5. A++lications o- neural networs

5.1 Neural networs in +ractice

5.# Neural networs in *edicine

5.#.1 6odellin% and 7ia%nosin% t!e Cardio)ascular S'ste*5.#.# Electronic noses , detection and reconstruction o- odours b' ANNs

5.#.& Instant 0!'sician , a co**ercial neural net dia%nostic +ro%ra*

5.& Neural networs in business

5.&.1 6aretin%

5.&.# Credit e)aluation

8. Conclusion

Re-erences

A++endi A , $istorical bac%round in detail

A++endi , T!e bac +ro+o%ation al%orit!* , *at!e*atical a++roac!

A++endi C , Re-erences used t!rou%!out t!e re)iew
http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Introduction%20to%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#What%20is%20a%20Neural%20Networkhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Historical%20backgroundhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Why%20use%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20networks%20versus%20conventional%20computershttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Human%20and%20Artificial%20Neurones%20-%20investigating%20the%20similaritieshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#How%20the%20Human%20Brain%20Learnshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#%20From%20Human%20Neurones%20to%20Artificial%20Neuroneshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#An%20engineering%20approachhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#A%20simple%20neuronhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#%20Firing%20ruleshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Pattern%20Recognition%20-%20an%20examplehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#A%20more%20complicated%20neuronhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Architecture%20of%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Feed-forward%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Feedback%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Network%20layershttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Perceptronshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#The%20Learning%20Processhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Transfer%20Functionhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Transfer%20Functionhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#An%20Example%20to%20illustrate%20the%20above%20teaching%20procedurehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#An%20Example%20to%20illustrate%20the%20above%20teaching%20procedurehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#The%20Back-Propagation%20Algorithmhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Applications%20of%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20Networks%20in%20Practice%20http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20networks%20in%20medicinehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Modelling%20and%20Diagnosing%20the%20Cardiovascular%20Systemhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Electronic%20noseshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Electronic%20noseshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Instant%20Physicianhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Instant%20Physicianhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20Networks%20in%20businesshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Marketinghttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Credit%20Evaluationhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Conclusionhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Referenceshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20A%20-%20Historical%20background%20in%20detailhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20B%20-%20The%20back-propagation%20Algorithm%20-%20a%20mathematical%20approachhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20C%20-%20References%20used%20throughout%20the%20reviewhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#What%20is%20a%20Neural%20Networkhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Historical%20backgroundhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Why%20use%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20networks%20versus%20conventional%20computershttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Human%20and%20Artificial%20Neurones%20-%20investigating%20the%20similaritieshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#How%20the%20Human%20Brain%20Learnshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#%20From%20Human%20Neurones%20to%20Artificial%20Neuroneshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#An%20engineering%20approachhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#A%20simple%20neuronhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#%20Firing%20ruleshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Pattern%20Recognition%20-%20an%20examplehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#A%20more%20complicated%20neuronhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Architecture%20of%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Feed-forward%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Feedback%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Network%20layershttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Perceptronshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#The%20Learning%20Processhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Transfer%20Functionhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#An%20Example%20to%20illustrate%20the%20above%20teaching%20procedurehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#The%20Back-Propagation%20Algorithmhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Applications%20of%20neural%20networkshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20Networks%20in%20Practice%20http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20networks%20in%20medicinehttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Modelling%20and%20Diagnosing%20the%20Cardiovascular%20Systemhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Electronic%20noseshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Instant%20Physicianhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Neural%20Networks%20in%20businesshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Marketinghttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Credit%20Evaluationhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Conclusionhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Referenceshttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20A%20-%20Historical%20background%20in%20detailhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20B%20-%20The%20back-propagation%20Algorithm%20-%20a%20mathematical%20approachhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Appendix%20C%20-%20References%20used%20throughout%20the%20reviewhttp://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html#Introduction%20to%20neural%20networks


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1. Introduction to neural networs

1.1 W!at is a Neural Networ"

An Artificial Neural Network "ANN# is an information processing paradigm that is inspired by the

way biological nervous systems such as the brain process information. The key element of thisparadigm is the novel structure of the information processing system. $t is composed of a large

number of highly interconnected processing elements "neurones# working in unison to solve

specific problems. ANNs like people learn by example. An ANN is configured for a specificapplication such as pattern recognition or data classification through a learning process. %earning

in biological systems involves ad&ustments to the synaptic connections that exist between the

neurones. This is true of ANNs as well.

1.# $istorical bac%round

Neural network simulations appear to be a recent development. 'owever this field was established

before the advent of computers and has survived at least one ma&or setback and several eras.

(any important advances have been boosted by the use of inexpensive computer emulations.

!ollowing an initial period of enthusiasm the field survived a period of frustration and disrepute.During this period when funding and professional support was minimal important advances were

made by relatively few researchers. These pioneers were able to develop convincing technologywhich surpassed the limitations identified by (insky and )apert. (insky and )apert published a

book "in *+,+# in which they summed up a general feeling of frustration "against neural networks#

among researchers and was thus accepted by most without further analysis. Currently the neural

network field en&oys a resurgence of interest and a corresponding increase in funding.

The first artificial neuron was produced in *+- by the neurophysiologist /arren (cCulloch and

the logician /alter )its. 0ut the technology available at that time did not allow them to do too

much.

1.& W!' use neural networs"

Neural networks with their remarkable ability to derive meaning from complicated or imprecise

data can be used to extract patterns and detect trends that are too complex to be noticed by eitherhumans or other computer techni1ues. A trained neural network can be thought of as an 2expert2 in

the category of information it has been given to analyse. This expert can then be used to provide

pro&ections given new situations of interest and answer 2what if2 1uestions.3ther advantages include4

*. Adaptive learning4 An ability to learn how to do tasks based on the data given for training or

initial experience.5. Self63rganisation4 An ANN can create its own organisation or representation of the

information it receives during learning time.

. 7eal Time 3peration4 ANN computations may be carried out in parallel and special

hardware devices are being designed and manufactured which take advantage of thiscapability.

-. !ault Tolerance via 7edundant $nformation Coding4 )artial destruction of a network leads tothe corresponding degradation of performance. 'owever some network capabilities may be

retained even with ma&or network damage.


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1.( Neural networs )ersus con)entional co*+uters

Neural networks take a different approach to problem solving than that of conventional computers.Conventional computers use an algorithmic approach i.e. the computer follows a set of instructions

in order to solve a problem. 8nless the specific steps that the computer needs to follow are known

the computer cannot solve the problem. That restricts the problem solving capability of

conventional computers to problems that we already understand and know how to solve. 0utcomputers would be so much more useful if they could do things that we don9t exactly know how to

do.

Neural networks process information in a similar way the human brain does. The network iscomposed of a large number of highly interconnected processing elements "neurones# working in

parallel to solve a specific problem. Neural networks learn by example. They cannot be

programmed to perform a specific task. The examples must be selected carefully otherwise usefultime is wasted or even worse the network might be functioning incorrectly. The disadvantage is that

because the network finds out how to solve the problem by itself its operation can be unpredictable.

3n the other hand conventional computers use a cognitive approach to problem solving: the waythe problem is to solved must be known and stated in small unambiguous instructions. Theseinstructions are then converted to a high level language program and then into machine code that

the computer can understand. These machines are totally predictable: if anything goes wrong is due

to a software or hardware fault.

Neural networks and conventional algorithmic computers are not in competition but complementeach other. There are tasks are more suited to an algorithmic approach like arithmetic operations

and tasks that are more suited to neural networks. ;ven more a large number of tasks re1uire

systems that use a combination of the two approaches "normally a conventional computer is used tosupervise the neural network# in order to perform at maximum efficiency.

Neural networks do not perform miracles. But if used sensibly they can produce some amazing

results.

#. $u*an and Arti-icial Neurones , in)esti%atin% t!e si*ilarities

#.1 $ow t!e $u*an rain Learns"

(uch is still unknown about how the brain trains itself to process information so theories abound.

$n the human brain a typical neuron collects signals from others through a host of fine structurescalled dendrites. The neuron sends out spikes of electrical activity through a long thin stand known

as an axon which splits into thousands of branches. At the end of each branch a structure called a

synapseconverts the activity from the axon into electrical effects that inhibit or excite activity in theconnected neurones. /hen a neuron receives excitatory input that is sufficiently large compared

with its inhibitory input it sends a spike of electrical activity down its axon. %earning occurs by

changing the effectiveness of the synapses so that the influence of one neuron on another changes.


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Components of a neuronThe synapse

#.# /ro* $u*an Neurones to Arti-icial Neurones

/e conduct these neural networks by first trying to deduce the essential features of neurones and

their interconnections. /e then typically program a computer to simulate these features. 'oweverbecause our knowledge of neurones is incomplete and our computing power is limited our modelsare necessarily gross idealisations of real networks of neurones.

The neuron model

&. An en%ineerin% a++roac!

&.1 A si*+le neuron

An artificial neuron is a device with many inputs and one output. The neuron has two modes ofoperation: the training mode and the using mode. $n the training mode the neuron can be trained to

fire "or not# for particular input patterns. $n the using mode when a taught input pattern is detected

at the input its associated output becomes the current output. $f the input pattern does not belong inthe taught list of input patterns the firing rule is used to determine whether to fire or not.


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A simple neuron

&.# /irin% rules

The firing rule is an important concept in neural networks and accounts for their high flexibility. A

firing rule determines how one calculates whether a neuron should fire for any input pattern. $trelates to all the input patterns not only the ones on which the node was trained.

A simple firing rule can be implemented by using 'amming distance techni1ue. The rule goes as

follows4

Take a collection of training patterns for a node some of which cause it to fire "the *6taught set of

patterns# and others which prevent it from doing so "the


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The difference between the two truth tables is called thegeneralisation of the neuron.Therefore thefiring rule gives the neuron a sense of similarity and enables it to respond 9sensibly9 to patterns not

seen during training.

&.& 0attern Reco%nition , an ea*+le

An important application of neural networks is pattern recognition. )attern recognition can beimplemented by using a feed6forward "figure *# neural network that has been trained accordingly.

During training the network is trained to associate outputs with input patterns. /hen the network isused it identifies the input pattern and tries to output the associated output pattern. The power of

neural networks comes to life when a pattern that has no output associated with it is given as an

input. $n this case the network gives the output that corresponds to a taught input pattern that isleast different from the given pattern.

!igure *.

!or example4

The network of figure * is trained to recognise the patterns T and '. The associated patterns are allblack and all white respectively as shown below.

$f we represent black s1uares with < and white s1uares with * then the truth tables for the

neurones after generalisation are:

=**4 < < < < * * * *

=*54 < < * * < < * *

=*4 < * < * < * < *

38T4 < < * * < < * *

To+ neuron


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=5*4 < < < < * * * *

=554 < < * * < < * *

=54 < * < * < * < *

38T4 * * * * * < * or threshold. arious algorithms exist that cause the neuron to 9adapt9: the most used ones are

the Delta rule and the back error propagation. The former is used in feed6forward networks and the

latter in feedback networks.

( Arc!itecture o- neural networs

(.1 /eed,-orward networs

!eed6forward ANNs "figure *# allow signals to travel one way only: from input to output. There isno feedback "loops# i.e. the output of any layer does not affect that same layer. !eed6forward ANNs

tend to be straight forward networks that associate inputs with outputs. They are extensively used in

pattern recognition. This type of organisation is also referred to as bottom6up or top6down.

(.# /eedbac networs

!eedback networks "figure *# can have signals travelling in both directions by introducing loops in

the network. !eedback networks are very powerful and can get extremely complicated. !eedbacknetworks are dynamic: their 9state9 is changing continuously until they reach an e1uilibrium point.

They remain at the e1uilibrium point until the input changes and a new e1uilibrium needs to be

found. !eedback architectures are also referred to as interactive or recurrent although the latterterm is often used to denote feedback connections in single6layer organisations.


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!igure -.* An example of a simple

feedforward network

!igure -.5 An example of a complicated network

(.& Networ la'ers

The commonest type of artificial neural network consists of three groups or layers of units4 a layer

of 2in+ut2 units is connected to a layer of 2!idden2 units which is connected to a layer of 9out+ut2

units. "see !igure -.*#

The activity of the input units represents the raw information that is fed into the network.

The activity of each hidden unit is determined by the activities of the input units and the weightson the connections between the input and the hidden units.

The behaviour of the output units depends on the activity of the hidden units and the weights

between the hidden and output units.

This simple type of network is interesting because the hidden units are free to construct their ownrepresentations of the input. The weights between the input and hidden units determine when each

hidden unit is active and so by modifying these weights a hidden unit can choose what it

represents.

/e also distinguish single6layer and multi6layer architectures. The single6layer organisation inwhich all units are connected to one another constitutes the most general case and is of more

potential computational power than hierarchically structured multi6layer organisations. $n multi6

layer networks units are often numbered by layer instead of following a global numbering.

(.( 0erce+trons

The most influential work on neural nets in the ,


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!igure -.-

$n *+,+ (insky and )apert wrote a book in which they described the limitations of single layer

)erceptrons. The impact that the book had was tremendous and caused a lot of neural networkresearchers to loose their interest. The book was very well written and showed mathematically that

single layerperceptrons could not do some basic pattern recognition operations like determining theparity of a shape or determining whether a shape is connected or not. /hat they did not realiseduntil the B


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re%ularit' detectionin which units learn to respond to particular properties of the input patterns./hereas in asssociative mapping the network stores the relationships among patterns in regularity

detection the response of each unit has a particular 9meaning9. This type of learning mechanism is

essential for feature discovery and knowledge representation.

;very neural network posseses knowledge which is contained in the values of the connectionsweights. (odifying the knowledge stored in the network as a function of experience implies a

learning rule for changing the values of the weights.

$nformation is stored in the weight matrix / of a neural network. %earning is the determination ofthe weights. !ollowing the way learning is performed we can distinguish two ma&or categories of

neural networks4

-ied networsin which the weights cannot be changed ie d/>dtdt not


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The behaviour of an ANN "Artificial Neural Network# depends on both the weights and the input6output function "transfer function# that is specified for the units. This function typically falls into

one of three categories4

linear "or ramp#

thresholdsigmoid

!or linear units the output activity is proportional to the total weighted output.

!or t!res!old units the output is set at one of two levels depending on whether the total input isgreater than or less than some threshold value.

!or si%*oid units the output varies continuously but not linearly as the input changes. Sigmoid

units bear a greater resemblance to real neurones than do linear or threshold units but all three must

be considered rough approximations.

To make a neural network that performs some specific task we must choose how the units areconnected to one another "see figure -.*# and we must set the weights on the connections

appropriately. The connections determine whether it is possible for one unit to influence another.

The weights specify the strength of the influence.

/e can teach a three6layer network to perform a particular task by using the following procedure4

*. /e present the network with training examples which consist of a pattern of activities for

the input units together with the desired pattern of activities for the output units.

5. /e determine how closely the actual output of the network matches the desired output.

. /e change the weight of each connection so that the network produces a better

approximation of the desired output.

4.# An Ea*+le to illustrate t!e abo)e teac!in% +rocedure:

Assume that we want a network to recognise hand6written digits. /e might use an array of say 5E,sensors each recording the presence or absence of ink in a small area of a single digit. The network

would therefore need 5E, input units "one for each sensor# *< output units "one for each kind of

digit# and a number of hidden units.

!or each kind of digit recorded by the sensors the network should produce high activity in theappropriate output unit and low activity in the other output units.

To train the network we present an image of a digit and compare the actual activity of the *< output

units with the desired activity. /e then calculate the error which is defined as the s1uare of the

difference between the actual and the desired activities. Next we change the weight of eachconnection so as to reduce the error./e repeat this training process for many different images of

each different images of each kind of digit until the network classifies every image correctly.

To implement this procedure we need to calculate the error derivative for the weight ";/# in orderto change the weight by an amount that is proportional to the rate at which the error changes as the

weight is changed. 3ne way to calculate the ;/ is to perturb a weight slightly and observe how the

error changes. 0ut that method is inefficient because it re1uires a separate perturbation for each of

the many weights.

Another way to calculate the ;/ is to use the 0ack6propagation algorithm which is described

below and has become nowadays one of the most important tools for training neural networks. $t


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was developed independently by two teams one "!ogelman6Soulie Fallinari and %e Cun# in!rance the other "7umelhart 'inton and /illiams# in 8.S.

4.& T!e ac,0ro+a%ation Al%orit!*

$n order to train a neural network to perform some task we must ad&ust the weights of each unit in

such a way that the error between the desired output and the actual output is reduced. This process

re1uires that the neural network compute the error derivative of the weights "EW#. $n other words

it must calculate how the error changes as each weight is increased or decreased slightly. The backpropagation algorithm is the most widely used method for determining the EW.

The back6propagation algorithm is easiest to understand if all the units in the network are linear.The algorithm computes each EWby first computing the EA the rate at which the error changes as

the activity level of a unit is changed. !or output units the EAis simply the difference between the

actual and the desired output. To compute theEAfor a hidden unit in the layer &ust before the

output layer we first identify all the weights between that hidden unit and the output units to whichit is connected. /e then multiply those weights by the EAs of those output units and add the

products. This sum e1uals the EAfor the chosen hidden unit. After calculating all the EAs in the

hidden layer &ust before the output layer we can compute in like fashion the EAs for other layers

moving from layer to layer in a direction opposite to the way activities propagate through thenetwork. This is what gives back propagation its name. 3nce the EAhas been computed for a unit

it is straight forward to compute theEWfor each incoming connection of the unit. The EWis theproduct of the ;A and the activity through the incoming connection.

Note that for non6linear units "see Appendix C# the back6propagation algorithm includes an extra

step. 0efore back6propagating the EAmust be converted into the EI the rate at which the error

changes as the total input received by a unit is changed.

5. A++lications o- neural networs5.1 Neural Networs in 0ractice

Fiven this description of neural networks and how they work what real world applications are they

suited forG Neural networks have broad applicability to real world business problems. $n fact they

have already been successfully applied in many industries.

Since neural networks are best at identifying patterns or trends in data they are well suited for

prediction or forecasting needs including4

sales forecasting

industrial process control

customer researchdata validation

risk managementtarget marketing

0ut to give you some more specific examples: ANN are also used in the following specific

paradigms4 recognition of speakers in communications: diagnosis of hepatitis: recovery oftelecommunications from faulty software: interpretation of multimeaning Chinese words: undersea

mine detection: texture analysis: three6dimensional ob&ect recognition: hand6written word

recognition: and facial recognition.

5.# Neural networs in *edicine


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Artificial Neural Networks "ANN# are currently a 9hot9 research area in medicine and it is believedthat they will receive extensive application to biomedical systems in the next few years. At the

moment the research is mostly on modelling parts of the human body and recognising diseases

from various scans "e.g. cardiograms CAT scans ultrasonic scans etc.#.

Neural networks are ideal in recognising diseases using scans since there is no need to provide aspecific algorithm on how to identify the disease. Neural networks learn by example so the details

of how to recognise the disease are not needed. /hat is needed is a set of examples that are

representative of all the variations of the disease. The 1uantity of examples is not as important asthe 91uantity9. The examples need to be selected very carefully if the system is to perform reliably

and efficiently.

5.#.1 6odellin% and 7ia%nosin% t!e Cardio)ascular S'ste*

Neural Networks are used experimentally to model the human cardiovascular system. Diagnosis can

be achieved by building a model of the cardiovascular system of an individual and comparing itwith the real time physiological measurements taken from the patient. $f this routine is carried out

regularly potential harmful medical conditions can be detected at an early stage and thus make the

process of combating the disease much easier.

A model of an individual9s cardiovascular system must mimic the relationship among physiologicalvariables "i.e. heart rate systolic and diastolic blood pressures and breathing rate# at different

physical activity levels. $f a model is adapted to an individual then it becomes a model of the

physical condition of that individual. The simulator will have to be able to adapt to the features ofany individual without the supervision of an expert. This calls for a neural network.

Another reason that &ustifies the use of ANN technology is the ability of ANNs to provide sensor

fusion which is the combining of values from several different sensors. Sensor fusion enables the

ANNs to learn complex relationships among the individual sensor values which would otherwisebe lost if the values were individually analysed. $n medical modelling and diagnosis this implies

that even though each sensor in a set may be sensitive only to a specific physiological variableANNs are capable of detecting complex medical conditions by fusing the data from the individualbiomedical sensors.

5.#.# Electronic noses

ANNs are used experimentally to implement electronic noses. ;lectronic noses have several

potential applications in telemedicine. Telemedicine is the practice of medicine over long distancesvia a communication link. The electronic nose would identify odours in the remote surgical

environment. These identified odours would then be electronically transmitted to another site where

an door generation system would recreate them. 0ecause the sense of smell can be an important

sense to the surgeon telesmell would enhance telepresent surgery.For more information on telemedicine and telepresent surgery clickhere.

5.#.& Instant 0!'sician

An application developed in the mid6*+B


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5.& Neural Networs in business

0usiness is a diverted field with several general areas of specialisation such as accounting or

financial analysis. Almost any neural network application would fit into one business area or

financial analysis.There is some potential for using neural networks for business purposes including resource

allocation and scheduling. There is also a strong potential for using neural networks for database

mining that is searching for patterns implicit within the explicitly stored information in databases.

(ost of the funded work in this area is classified as proprietary. Thus it is not possible to report onthe full extent of the work going on. (ost work is applying neural networks such as the 'opfield6

Tank network for optimiHation and scheduling.

5.&.1 6aretin%

There is a marketing application which has been integrated with a neural network system. The

Airline (arketing Tactician "a trademark abbreviated as A(T# is a computer system made of

various intelligent technologies including expert systems. A feedforward neural network is

integrated with the A(T and was trained using back6propagation to assist the marketing control ofairline seat allocations. The adaptive neural approach was amenable to rule expression. Additionaly

the application9s environment changed rapidly and constantly which re1uired a continuouslyadaptive solution. The system is used to monitor and recommend booking advice for eachdeparture. Such information has a direct impact on the profitability of an airline and can provide a

technological advantage for users of the system. I'utchison J Stephens *+BKL

/hile it is significant that neural networks have been applied to this problem it is also important to

see that this intelligent technology can be integrated with expert systems and other approaches tomake a functional system. Neural networks were used to discover the influence of undefined

interactions by the various variables. /hile these interactions were not defined they were used by

the neural system to develop useful conclusions. $t is also noteworthy to see that neural networkscan influence the bottom line.

5.&.# Credit E)aluation

The 'NC company founded by 7obert 'echt6Nielsen has developed several neural network

applications. 3ne of them is the Credit Scoring system which increase the profitability of theexisting model up to 5KM. The 'NC neural systems were also applied to mortgage screening. A

neural network automated mortgage insurance underwritting system was developed by the Nestor

Company. This system was trained with E


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Neural networks also contribute to other areas of research such as neurology and psychology. Theyare regularly used to model parts of living organisms and to investigate the internal mechanisms of

the brain.

)erhaps the most exciting aspect of neural networks is the possibility that some day 9consious9

networks might be produced. There is a number of scientists arguing that conciousness is a9mechanical9 property and that 9consious9 neural networks are a realistic possibility.

!inally $ would like to state that even though neural networks have a huge potential we will onlyget the best of them when they are intergrated with computing A$ fuHHy logic and related sub&ects.

Re-erences:

*. An introduction to neural computing. Aleksander $. and (orton '. 5nd edition

5. Neural Networks at )acific Northwest National %aboratory

http4>>www.emsl.pnl.gov45cie>neural>neural.homepage.html

. $ndustrial Applications of Neural Networks "research reports ;sprit $.!.Croall O.).(ason#

-. A Novel Approach to (odelling and Diagnosing the Cardiovascular System

http4>>www.emsl.pnl.gov45cie>neural>papers5>keller.wcnn+E.abs.html

E. Artificial Neural Networks in (edicine

http4>>www.emsl.pnl.gov45cie>techbrief>NN.techbrief.ht

,. Neural Networks by ;ric Davalo and )atrick Naim

K. %earning internal representations by error propagation by 7umelhart 'inton and /illiams

"*+B,#.

B. limasauskas CC. "*+B+#. The *+B+ Neuro Computing 0ibliography. 'ammerstrom D.

"*+B,#. A Connectionist>Neural Network 0ibliography.

+. DA7)A Neural Network Study "3ctober *+BK6!ebruary *+B+#. ($T %incoln %ab. Neural

Networks ;ric Davalo and )atrick Naim

*


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A++endi A , $istorical bac%round in detail

The history of neural networks that was described above can be divided into several periods4

*. /irst Atte*+ts:There were some initial simulations using formal logic. (cCulloch and

)itts "*+-# developed models of neural networks based on their understanding of

neurology. These models made several assumptions about how neurons worked. Theirnetworks were based on simple neurons which were considered to be binary devices with

fixed thresholds. The results of their model were simple logic functions such as 2a or b2 and

2a and b2. Another attempt was by using computer simulations. Two groups "!arley andClark *+E-: 7ochester 'olland 'aibit and Duda *+E,#. The first group "$0( reserchers#

maintained closed contact with neuroscientists at (cFill 8niversity. So whenever their

models did not work they consulted the neuroscientists. This interaction established amultidiscilinary trend which continues to the present day.

5. 0ro*isin% E*er%in% Tec!nolo%':Not only was neroscience influential in thedevelopment of neural networks but psychologists and engineers also contributed to the

progress of neural network simulations. 7osenblatt "*+EB# stirred considerable interest andactivity in the field when he designed and developed the )erceptron. The )erceptron had

three layers with the middle layer known as the association layer.This system could learn to

connect or associate a given input to a random output unit.Another system was the ADA%$N; "ADAptive %$near ;lement# which was developed in

*+,< by /idrow and 'off "of Stanford 8niversity#. The ADA%$N; was an analogue

electronic device made from simple components. The method used for learning wasdifferent to that of the )erceptron it employed the %east6(ean6S1uares "%(S# learning

rule.

. 0eriod o- /rustration 7isre+ute:$n *+,+ (insky and )apert wrote a book in which

they generalised the limitations of single layer )erceptrons to multilayered systems. $n the

book they said4 2...our intuitive &udgment that the extension "to multilayer systems# is

sterile2. The significant result of their book was to eliminate funding for research withneural network simulations. The conclusions supported the disenhantment of reserchers in

the field. As a result considerable pre&udice against this field was activated.

-. Inno)ation:Although public interest and available funding were minimal several

researchers continued working to develop neuromorphically based computaional methods

for problems such as pattern recognition.During this period several paradigms were generated which modern work continues to

enhance.Frossberg9s "Steve Frossberg and Fail Carpenter in *+BB# influence founded aschool of thought which explores resonating algorithms. They developed the A7T "Adaptive

7esonance Theory# networks based on biologically plausible models. Anderson andohonen developed associative techni1ues independent of each other. lopf "A. 'enry

lopf# in *+K5 developed a basis for learning in artificial neurons based on a biological

principle for neuronal learning called heterostasis./erbos ")aul /erbos *+K-# developed and used the back6propagation learning method

however several years passed before this approach was populariHed. 0ack6propagation nets

are probably the most well known and widely applied of the neural networks today. $nessence the back6propagation net. is a )erceptron with multiple layers a different thershold

function in the artificial neuron and a more robust and capable learning rule.


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Amari "A. Shun6$chi *+,K# was involved with theoretical developments4 he published apaper which established a mathematical theory for a learning basis "error6correction method#

dealing with adaptive patern classification. /hile !ukushima "!. unihiko# developed a step

wise trained multilayered neural network for interpretation of handwritten characters. The

original network was published in *+KE and was called the Cognitron.

E. Re,E*er%ence:)rogress during the late *+K


19/20

where yiis the activity level of the &th unit in the previous layer and / i&is the weight of the

connection between the ith and the &th unit.

Next the unit calculates the activity y&using some function of the total weighted input. Typically

we use the sigmoid function4

3nce the activities of all output units have been determined the network computes the error ;which is defined by the expression4

where y&is the activity level of the &th unit in the top layer and d&is the desired output of the &th unit.

The back6propagation algorithm consists of four steps4

*. Compute how fast the error changes as the activity of an output unit is changed. This errorderivative ";A# is the difference between the actual and the desired activity.

5. Compute how fast the error changes as the total input received by an output unit is changed. This

1uantity ";$# is the answer from step * multiplied by the rate at which the output of a unit changesas its total input is changed.

. Compute how fast the error changes as a weight on the connection into an output unit is changed.

This 1uantity ";/# is the answer from step 5 multiplied by the activity level of the unit from which

the connection emanates.

-. Compute how fast the error changes as the activity of a unit in the previous layer is changed. This

crucial step allows back propagation to be applied to multilayer networks. /hen the activity of aunit in the previous layer changes it affects the activites of all the output units to which it is

connected. So to compute the overall effect on the error we add together all these seperate effects

on output units. 0ut each effect is simple to calculate. $t is the answer in step 5 multiplied by theweight on the connection to that output unit.


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0y using steps 5 and - we can convert the ;As of one layer of units into ;As for the previous

layer. This procedure can be repeated to get the ;As for as many previous layers as desired. 3ncewe know the ;A of a unit we can use steps 5 and to compute the ;/s on its incoming

connections.

A++endi C , Re-erences used t!rou%!out t!e re)iew

*. An introduction to neural computing. Aleksander $. and (orton '. 5nd edition

5. Neural Networks at )acific Northwest National %aboratory

http4>>www.emsl.pnl.gov45cie>neural>neural.homepage.html

. Artificial Neural Networks in (edicine

http4>>www.emsl.pnl.gov45cie>techbrief>NN.techbrief.ht

-. $ndustrial Applications of Neural Networks "research reports ;sprit $.!.Croall O.).(ason#

E. A Novel Approach to (odelling and Diagnosing the Cardiovascular Systemhttp4>>www.emsl.pnl.gov45cie>neural>papers5>keller.wcnn+E.abs.html

,. ;lectronic Noses for Telemedicine

http4>>www.emsl.pnl.gov45cie>neural>papers5>keller.ccc+E.abs.html

K. An $ntroduction to Computing with Neural Nets "7ichard ). %ipmann $;;; ASS)

(agaHine April *+BK#

B. )attern 7ecognition of )athology $mages

http4>>kopernik6eth.npac.syr.edu4*5pattern.html

+. Developments in autonomous vehicle navigation. Stefan Neuber Oos Ni&huis %ambertSpaanenburg. $nstitut fur (ikroelektronik Stuttgart Allmandring

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