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Learning Algorithm and

Neural Networks

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MTR 607

Textbook:Simon Haykin, Neural Networks A Comprehensive

Foundation, 2nd Ed., 1999

Lecturer:Dr. Alaa Sagheer

Place:Seminar Room, E-JUST

Grading: Class participation (10%),

Assignments and reports (20%),

Midterm test (30%),

Final exam (40%)

2

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Course OverviewIntroduction to Artificial Neural Networks,

Artificial and human neurons (Biological Inspiration)

The learning process,

Supervised and unsupervised learning,

Reinforcement learning,

Applications Development and Portfolio

The McCulloch-Pitts Model of Neuron,

A simple network layers, Multilayer networks

Perceptron,

Back propagation algorithm,

Recurrent networks,Associative memory,

Self Organizing maps,

Support Vector Machine and PCA,

Applications to speech, vision and control problems.

3MTR607: Learning Algorithms and Neural Networks Dr. Alaa Sagheer

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ANNs ResourcesMain text books:

Neural Networks: A Comprehensive Foundation

, S. Haykin(very good -

theoretical)

Pattern Recognition with Neural Networks, C. Bishop (very good-more accessibleNeural Network Design by Hagan, Demuth and Beale (introductory)

Books emphasizing the practical aspects:

Neural Smithing, Reeds and MarksPractical Neural Network Recipees in C++ T. Masters

Seminal Paper:

Parallel Distributed Processing Rumelhart and McClelland et al.

Other:

Neural and Adaptive Systems, J. Principe, N. Euliano, C. Lefebvre


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Review Articles:R. P. Lippman, An introduction to Computing with Neural Nets IEEE ASPMagazine, 4-22, April 1987.

T. Kohonen, An Introduction to Neural Computing, Neural Networks, 1, 3-16, 1988.A. K. Jain, J. Mao, K. Mohuiddin, Artificial Neural Networks: A Tutorial IEEEComputer, March 1996 p. 31-44.

ANNs Resources


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Course OverviewIntroduction to Artificial Neural Networks,

Artificial and human neurons (Biological Inspiration)The learning process,

Supervised and unsupervised learning,

Reinforcement learning,

Applications Development and Portfolio

The McCulloch-Pitts Model of Neuron,A simple network layers, Multilayer networks

Perceptron,

Back propagation algorithm,

Recurrent networks,

Associative memory,Self Organizing maps,

Support Vector Machine and PCA,

Applications to speech, vision and control problems.


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Part I:

1. Artificial Neural Networks

2. Artificial and human neurons (Biological Inspiration)

3. Tasks & Applications of ANNs

Part II:

1. Learning in Biological Systems

2. Learning with Artificial Neural Networks

Introduction to Artificial Neural Networks


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ANNs vs. ComputersDigital Computers

Analyze the problem to be solved

Deductive Reasoning. We applyknown rules to input data to produce

output.

Computation is centralized,synchronous, and serial.

Not fault tolerant. One transistor goesand it no longer works.

Static connectivity.

Applicable if well defined rules withprecise input data.


Artificial Neural Networks

No requirements of an explicit

description of the problem.

Inductive Reasoning. Given input and

output data (training examples), we

construct the rules.

Computation is collective,asynchronous, and parallel.

Fault tolerant and sharing of

responsibilities.

Dynamic connectivity.

Applicable if rules are unknown or

complicated, or if data are noisy or

partial.

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What is ANN?


ANN is a branch of "Artificial Intelligence". It is a system modeled based on the human brain.ANN goes by many names, such as connectionism, parallel distributed processing, neuro-computing, machine learning algorithms, and finally, artificial neural networks.

Developing ANNs date back to the early 1940s. It experienced a wide popularity in the late

1980s. This was a result of the discovery of new techniques and developments in PCs.

Some ANNs are models of biological neural networks and some are not.

ANN is a processing device (An algorithm or Actual hardware) whose design was motivated by

the design and functioning of human brain.

Inside ANN:

ANNs design is what distinguishes neural networks from other mathematical techniquesANN is a network of many simple processors ("units or neurons), each unit has a smallamount of local memory.

The units are connected by unidirectional communication channels ("connections"), whichcarry numeric (as opposed to symbolic) data.

The units operate only on their local data and on the inputs they receive via the connections.

Artificial Neural Networks (1)

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ANNs Operation

ANNs normally have great potential for parallelism (multiprocessor-friendly architecture),

since the computations of the units are independent of each other. Same like biological neuralnetworks.

Most neural networks have some kind of "training" rule whereby the weights of connections areadjusted on the basis of presented patterns.

In other words, neural networks "learn" from examples, just like childrenand exhibit somestructural capability for generalization.



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ANNs are a powerful technique (Black Box) to solve many real world

problems. They have the ability to learn from experience in order toimprove their performance and to adapt themselves to changes in the

environment.

In addition, they are able to deal with incomplete information or

noisy data and can be very effective especially in situations where it is

not possible to define the rules or steps that lead to the solution of aproblem.

Once trained, the ANN is able to recognize similarities when

presented with a new input pattern, resulting in a predicted output

pattern.



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What can a ANN do?

Compute a known function

Approximate an unknown function

Pattern Recognition

Signal Processing

.Learn to do any of the above

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Part I:

1. Artificial Neural Networks (ANNs)



Part II:





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Biological Inspiration

Animals are able to react adaptively to changes in their external

and internal environment, and they use their nervous system toperform these behaviours.

An appropriate model/simulation of the nervous system shouldbe able to produce similar responses and behaviours in artificialsystems.

The nervous system is build by relatively simple units, theneurons, so copying their behaviour and functionality should bethe solution!

Biological Neural Networks (BNN) are much more

complicated in their elementary structures than the

mathematical models we use for ANNs


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ANN as a model of brain-

like Computer

Brain

The human brain is still not well

understood and indeed its behavior

is very complex!

There are about 10-11 billion

neurons in the human cortex each

connected to , on average, 10000others. In total 60 trillion synapses

of connections.

The brain is a highly complex,

nonlinear and parallel computer

(information-processing system)

ANN as a Brain-Like Computer


An artificial neural network (ANN) is

a massively parallel distributed processor

that has a natural propensity for storingexperimental knowledge and making it

available for use. It means that:

Knowledge is acquired by the network

through a learning (training) process;

The strength of the interconnections

between neurons is implemented by

means of the synaptic weights used to

store the knowledge.

The learning process is a procedure of theadapting the weights with a learning

algorithm in order to capture the knowledge.

On more mathematically, the aim of the

learning process is to map a given relation

between inputs and output of the network.

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Massive parallelism

Brain computer as an information

or signal processing system, is

composed of a large number of a

simple processing elements, calledneurons. These neurons are

interconnected by numerous direct

links, which are called connection,

and cooperate which other to

perform a parallel distributed

processing (PDP) in order to soft a

desired computation tasks.

Connectionism

Brain computer is a highly

interconnected neurons system in

such a way that the state of one

neuron affects the potential of thelarge number of other neurons

which are connected according to

weights or strength. The key idea

of such principle isthe functional

capacity of biological neural nets

deters mostly not so of a single

neuron but of its connections

Associative

distributed memory

Storage of information in a brain is

supposed to be concentrated insynaptic connections of brain

neural network, or more precisely,

in the pattern of these connections

and strengths (weights) of the

synaptic connections.

A process of pattern

recognition and pattern

manipulation is based on:

How our brainmanipulates

with patterns ?

Principles of Brain Processing


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Biological

Neuron

- The simple

arithmeticcomputing

element

Biological Neuron

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Cell structures

Cell body

DendritesAxon

Synaptic terminals

Biological Neuron (2)


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synapses

axon dendrites

The information transmission happens at the synapses, i.e

Synaptic connection strengths among neurons are used to storethe acquired knowledge.

In a biological system, learning involves adjustments to the

synaptic connections between neurons


Biological Neurons (3)

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Biological Neurons (4)


1. Soma or body cell - is a large, round

central body in which almost all the

logical functions of the neuron are

realized (i.e. the processing unit).

2. The axon (output), is a nerve fibre

attached to the soma which can serve

as a final output channel of the

neuron. An axon is usually highly

branched.

3. The dendrites (inputs)- represent a

highly branching tree of fibers. These

long irregularly shaped nerve fibers

(processes) are attached to the soma

carrying electrical signals to the cell

4. Synapses are the point of contact

between the axon of one cell and the

dendrite of another, regulating a

chemical connection whose strength

affects the input to the cell.

The schematic

model of a

biological neuron

Synapses

Dendrites

Soma

AxonDendrite

from

other

Axon from

other

neuron

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Properties of ANNs

Learning from examples

labeled or unlabeled

Adaptivity

changing the connection strengths to learn things

Non-linearity

the non-linear activation functions are essential

Fault tolerance

if one of the neurons or connections is damaged, the

whole network still works quite well

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Part I:

1. Artificial Neural Networks (ANNs)



Part II:





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Applications of ANNsClassification

In marketing: consumer spending pattern classification

In defence: radar and sonar image classification

In agriculture & fishing: fruit, fish and catch grading

In medicine: ultrasound and electrocardiogram image classification, EEGs, medical diagnosis

Recognition and Identification

In general computing and telecommunications: speech, vision and handwriting recognition

In finance: signature verification and bank note verificationAssessment

In engineering: product inspection monitoring and control

In defence: target tracking

In security: motion detection, surveillance image analysis and fingerprint matching

Forecasting and Prediction

In finance: foreign exchange rate and stock market forecasting

In agriculture: crop yield forecasting , Deciding the category of potential food items

(e.g., edible or non-edible)

In marketing: sales forecasting

In meteorology: weather prediction

MTR607: Learning Algorithms and Neural Networks Dr. Alaa Sagheer 23

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Who are the Men of ANNs?!Computer scientists want to find out about the properties of non-symbolicinformation processing with neural nets and about learning systems ingeneral.

Statisticians use neural nets as flexible, nonlinear regression andclassification models.

Engineers of many kinds exploit the capabilities of neural networks in manyareas, such as signal processing and automatic control.

Cognitive scientists view neural networks as a possible apparatus to describemodels of thinking and consciousness (High-level brain function).

Neuro-physiologists use neural networks to describe and explore medium-level brain function (e.g. memory, sensory system, motorics).

Physicists use neural networks to model phenomena in statistical mechanics

and for a lot of other tasks.Biologists use Neural Networks to interpret nucleotide sequences.

Philosophers and some other people may also be interested in NeuralNetworks for various reasons


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Operation of Biological Neuron

The spikes travelling along the axon of the pre-synaptic neurontrigger the release of neurotransmitter substances at thesynapse.

The neurotransmitters cause excitation or inhibition in thedendrite of the post-synaptic neuron.

The integration of the excitatory and inhibitory signals mayproduce spikes in the post-synaptic neuron.

The contribution of the signals depends on the strength of thesynaptic connection.


Excitation means positive product between the incoming

spike rate and the corresponding synaptic weight;

Inhibition means negative product between the incomingspike rate and the corresponding synaptic weight;

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Inputs

Output

An artificial neural network is composed of many

artificial neurons that are linked together accordingto a specific network architecture. The objective of

the neural network is to transform the inputs into

meaningful outputs.

ANN Architecture


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Neurons are arranged in layers. Neurons work by processing information. They

receive and provide information in form of spikes.


The artificial neuron receives one or more inputs (representing the one or more

dendrites),

At each neuron, every input has an associated weight which modifies the

strength of each input and sums them together,

The sum of each neuron is passed through a function known as an activation

function ortransfer function in order to produce an output (representing a

biological neuron's axon)

ANN Architecture (2)

Inputs Output
http://en.wikipedia.org/wiki/Dendritehttp://en.wikipedia.org/wiki/Activation_functionhttp://en.wikipedia.org/wiki/Activation_functionhttp://en.wikipedia.org/wiki/Transfer_functionhttp://en.wikipedia.org/wiki/Axonhttp://en.wikipedia.org/wiki/Axonhttp://en.wikipedia.org/wiki/Transfer_functionhttp://en.wikipedia.org/wiki/Activation_functionhttp://en.wikipedia.org/wiki/Activation_functionhttp://en.wikipedia.org/wiki/Dendrite

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Input

s

Outputw2

w1

w3

wn

wn-1

. . .

x1

x2

x3

xn-1

xn

y)(;

1

zHyxwzn

i

ii

Each neuron takes one or more inputs and produces an output. At eachneuron, every input has an associated weight which modifies the strength of

each input. The neuron simply adds together all the inputs and calculates an

output to be passed on.


ANN Architecture (3)

f A

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Models of A Neuron


M d l f A N (2)

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Axon

Terminal Branches

of AxonDendrites

S

x1

x2

w1

w2

wn

xn

x3 w3

Models of A Neuron (2)


M d l f A N (3)

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1. A set of synapses, or connection link: each of whichis characterized by a weight or strength of its own wkj.

Specifically, a signal xj at the input synapse j connected toneuron k is multiplied by the synaptic wkj

2. An adder: For summing the input signals, weighted byrespective synaptic strengths of the neuron in a linear

operation.

3. Activation function: For limiting of the amplitude of theoutput of the neuron to limited range. The activation function

is referred to as a Squashing (i.e. limiting) function {interval

[0,1], or, alternatively [-1,1]}

Models of A Neuron (3)

Three elements:


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BiasThe bias has the effect of increasing or lowering the net input of

the activation function depending on whether it is +/-

yk= (vk) = (uk+ bk) = (S wkjxj + bk)An artificial neuron:

- computes the weighted sum of its input (called its net input)- adds its bias (the effect of applying affine transformation to the output vk)

- passes this value through an activation function

We say that the neuron fires (i.e. becomes active) if

its outputs is above zero.This extra free variable (bias) makes the neuron more

powerful.


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Activation Function (vk)It defines the output of the neuron given an input or set of inputs. A standard

computer chip circuit can be seen as a digital network of activation functions

that can be "ON" (1) or "OFF" (0), depending on input,

The best activation function is the non-linear function. Linear functions are

limited because the output is simply proportional to the input.


Three basic types of activation function:1. Threshold function,

2. Linear function,

3. Sigmoid function.

A ti ti f ti (2)

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Threshold (Step) function

The outputykof this activation function is binary, depending onwhether the input meets a specified threshold. The "signal" is sent,

i.e. the output is set to one, if the activation meets the threshold.

Activation functions (2)

McColloch-Pitts ModelThreshold Logic Unit

(TLU),since 194334MTR607: Learning Algorithms and Neural Networks Dr. Alaa Sagheer

A ti ti f ti (3)

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Piecewise Linear Function- The amplification factor inside the linear region of operation is assumed to beunity.

- This form may be viewed as an approximation to a non linear amplifier



A ti ti f ti (4)

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Sigmoid function

Where a is the slope parameter ofthe sigmoid function


- A fairly simple non-linear function, such as the logistic function.- As the slop parameter approaches infinity the sigmoid function becomes a

threshold function


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Artificial Neural Networks

Early ANN Models:

McCulloch-Pitts , Perceptron, ADALINE,

Hopfield Network,

Current Models:

Multilayer feed forward networks (Multilayer

perceptrons- Back propagation )

Radial Basis Function networks

Self Organizing Networks

...


F db k

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FeedbackFeedback is a dynamic system whenever occurs in

almost every part of the nervous system,

Feedback is giving one or more closed path for

transmission of signals around the system,

It plays important role in study of special class of

neural networks known as Recurrent networks.

F db k (2)

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Feedback (2)

The system is assumed to be linear and has a forward path (A)and a feedback path (B),

The output of the forward channel determines its own output

through the feedback channel.

F db k (3)

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Feedback (3)

E.g. considerA is a fixed weight and B is a unit delay operatorz-1 .

F db k (4)

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Feedback (4)

Then, we may expressyk(n) as an infinite weighted summation of

present and past samples of the input signalxj(n).

Therefore, feedback systems are controlled by weight.

F db k (5)

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Feedback (5)Feedback systems are controlled

by weight.

1. For positive weight, we have

stable systems, i,e, convergent

output y,

2. For negative weight, we have,

unstable systems, i.e divergent

output y.. (Linear andExponential)

N t k A hit t

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Network ArchitecturesThree different classes of network architectures:

1. Single-layer feed forward networks,

2. Multilayer feed forward networks,

3. Recurrent networks.

Si l l f d f d t k

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Single-layer feed forward network

- Input layer of source nodes that projects directly

onto an output layer of neurons.

- Single-layer referring to the output layer ofcomputation nodes (neuron).

M ltil f d f d t k

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Multilayer feed forward networkIt contains one or more hidden

layers (hidden neurons).Hidden refers to the part ofthe neural network is not seen

directly from either input or

output of the network .The function of hidden neuron

is to intervene between input

and output.

By adding one or more hiddenlayers, the network is able to

extract higher-order statistics

from input

R t N t k

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Recurrent NetworksIt is different from feed

forward neural network in thatit has at least one feedback

loop.

Recurrent network may consist

of single layer of neuron witheach neuron feeding its output

signal back to the inputs of all

the other neurons.Note: There

are no self-feedback.

Feedback loops have a

profound impact on learning

and overall performance.

H t D id N t k T l ?

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Slide 47

What transfer function should be used?

How many inputs does the network need?

How many hidden layers does the network need?

How many hidden neurons per hidden layer?

How many outputs should the network have?

There is no standard methodology to determinate these values.

Even there is some heuristic points, final values are

determinate by a trial and error procedure.

How to Decide on a Network Topology?

K l d R t ti

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Knowledge Representation

The main characteristic of knowledge representation has two

folds:

1) What information is actually made explicit?

2) How the information is physically encoded for subsequent use?

Knowledgeis referred to the stored information or models used

by a person or machine to interpret, predict and, appropriately,respond to the outside.

A good solution depends on a good representation of

knowledge

K l d R t ti (2)

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There are two kinds of Knowledge:1) The known world states, or facts, (prior knowledge),

2) Observations (measurements) of the world, obtained by

sensors to probe the environment.

Knowledge Representation (2)

These observations

represent the pool of

information, from

which examples areused to train the NN

K l d R t ti (3)

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These Examples can be labeled or unlabeled

In labeled examples

Each example representing an input signal is paired with a

corresponding desired response,

Labeled examples may be expensive to collect, as they requireavailability of a teacher to provide a desired response foreach labeled example.

Un labeled examples

Unlabeled examples are usually abundant as there is no needfor supervision.


K l d R t ti (3)

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Design of neural network may proceed as follow:An appropriate architecture for the neural network, with aninput layer consisting of source nodes equal in number to the

pixels of an input image.

The recognition performance of trained network is tested with

data not seen before (testing).

This phase of the network design called learning


R l f K l d R t ti

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Roles of Knowledge RepresentationThere are four rules for knowledge representation:

Rule 1:

Similar inputs (i.e., patterns) drawn from similar

classes should usually produce similar representation

inside the network, and should therefore be classified as

belonging to the same class.

There are plethora (many) of measures for

determining the similarity between inputs

R l f K l d R t ti (2)

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(1)

Roles of Knowledge Representation (2)A commonly used measure of similarity is the Euclidian Distance

Let xi denotes an m-by-1 vector


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Roles of Knowledge Representation (3)Another measure is the dot productorinner product com

Given a pair of vectors xi andxj of the same dimension, their innerproduct will be (the projection of vectorx

ionto vectorx

j)

Please note that:


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Using Eq.(1) to write

Roles of Knowledge Representation (4)The smaller the Euclidean distance x

i - x

j(i.e. the more similar

the vectorxi andxj are), the larger the inner product xiT

xj will be.To formalize this relationship, we normalizethe vectors x

i andx

jto have a unit length, i.e.:

The minimization of the Euclidean distance d(xi, xj ) corresponds

to maximization of the inner product (xi, x

j )..and, therefore, the

similarity between the vectors xi and xj


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If the vectors xi and x

jare stochastic (drown from different

population of data)

Roles of Knowledge Representation (5)

Where C-1 is the inverse of the covariance

matrix C. It is supposed that the

covariance matrix is the same for both

For a prescribed C, the smaller the distance d is themore similar the vectors xi and xj will be


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Rule 2:

Item to be categorized as separate classes should be given widelydifferent representation in work.

Rule 3:If a particular feature is important, then there should be large

number of neurons involved in the representation of that item inthe network.

Rule 4:Prior information and invariance should be built into the design of

a neural network when ever they are available, so as to simplifythe network design by its not having to learn them.

Roles of Knowledge Representation (6)

Rule 4 is particularly important and highly desirable

Roles of Kno ledge Representation (7)

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1) Biological visual and auditory networks are very specialized,

2) NN with SS has a smaller number of free parameters available for

adjustment than other networks. Then, they need a small training dataset,

learns faster and generalize better.

3) Rate of information transmission through a specialized network is faster,

4) Cost of building a specialized network is minimum, due to small size.

Roles of Knowledge Representation (7)Rule 4 is particularly important and highly desirable

because it results in an NN with a Specialized Structure (SS)

How to build prior information into NN design?

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How to build prior information into NN design?There are currently no well-defined rules for doing this; but wehave some procedure are known to yield useful rules. In particular,we may use a combination of two techniques:

1. Restricting the network architecture (using local connections)

2. Constraining the choice of synaptic weight (using the weightsharing)

The latter tech is so

important because it

leads to reducing

significantly freeparameters

How to build invariance into NNs design?

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How to build invariance into NNs design?

There are three technique for rendering classifier-type NNs

invariant to transformations:

1. Invariance by structure.

2. Invariance by training.

3. Invariance by feature space

Consider any of the following:

1) When an object rotates, the perceived image, by observer, will change as well,

2) The utterance of a spoken person may be soft or loud..slower or quicker,

3) ..

A classifier should be invariant to different transformation

Or

A class estimate represented by an output of the classifierMUST not be affected by transformations of the observed

signal applied to the classifier input

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Learning in

Biological Systems

Learning in Biological Systems

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Learning in Biological Systems

Learning approach based on modeling adaptation in

biological neural systems

Learning = learning by adaptation

The young animal learns that the green fruits are sour,

while the yellowish/reddish ones are sweet. The

learning happens by adapting the fruit picking

behaviour

Learning in Biological Systems (2)

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From experience: examples / training data

Learning happens by changing of the synaptic

strengths,

Synapses change size and strength with experience (or

examples or training data),

Strength of connection between the neurons is stored

as a weight-value for the specific connection,

Learning the solution to a problem = changing the

connection weights



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Hebbian Learning

When two connected neurons are firing at the same

time, the strength of the synapse between them

increases,

Neurons that fire together, wire together


Learning in ANN

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Learning in ANNWe may categorize the learning process through Neural

Networks function as follows:

1. Learning with a teacher,

- Supervised Learning

2. Learning without a teacher,

- Unsupervised Learning

- Reinforcement Learning

Supervised Learning

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In supervised learning, both the

inputs and the outputs are

provided. The network then

processes the inputs and compares

its resulting outputs against the

desired outputs

Errors are then calculated, causingthe system to adjust the weights

which control the network. This

process occurs over and over as the

weights are continually improved.

Supervised Learning

Supervised learning process

constitutes a closed-loop

feedback system but unknown

environment is outside the loop,

Supervised Learning (2)

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It is based on a labeled

training set.

The class of each piece

of data in training set is

known.

Class labels are pre-

determined and

provided in the trainingphase.

A

B

A

BA

B

Class

Class

Class

Class

Class

Class

Supervised Learning (2)

Understanding Supervised Learning

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g p g

A

BA

B A

B

Two Possible Solutions

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Two Possible Solutions

A

B

A

B

A

B

A

B A

B

A

B

How to solve a given problem of supervised learning?

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How to solve a given problem of supervised learning?Various steps have to be considered:

1. Determine the type of training examples,

2. Gather a training data set that satisfactory describe the given problem,

3. After the training process we can test the performance of learned artificial

neural network with the test (validation) data set,

4. Test data set consist of data that has not been introduced to artificial

neural network while learning.

Reinforcement Learning

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Reinforcement Learning

The learning of inputoutputmapping is performed through

continued interaction with the

environment in order to minimize

a scalar index of performance.

Or

A machine learning technique

that sets parameters of an

artificial neural network, where

data is usually not given, but

generated by interactions with the

environment.

Reinforcement Learning (2)

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Reinforcement Learning (2)

Reinforcement learning is built around critic that converts primary

reinforcement signal received from the environment into a higher

quality reinforcement signal

Unsupervised Learning

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U supe v sed e g

No help from the outside,

No information available on the desired output,

Input: set of patterns P, from n-dimensional space S, but little /no information about their classification, evaluation, interestingfeatures, etc.

It must learn these by itself!

Learning by doingTasks: Used to pick out structure in the input

Clustering - Group patterns based on similarity,

Vector Quantization - Fully divide up S into a small set ofregions (defined by codebook vectors) that also helps cluster P,

Feature Extraction - Reduce dimensionality of S by removingunimportant features (i.e. those that do not help in clustering P)

Supervised vs. Unsupervised

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Supervised vs. Unsupervised

Task performed

Classification

Pattern Recognition

NN model

Preceptron,Feed-Forward NN

Task performed

Clustering, Pattern Recognition

Feature Extraction, VQ

NN Model

Self Organizing Maps,ART

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MTR607 Chapter 0