PROGRAM NAME : B.TECH CSE

COURSE NAME: MACHINE LEARNING

NEURAL NETWORKS

CONTENTS Introduction. Artificial Neural Networks. Model of Artificial Neurons. Neural Network Architecture. Single Layer Feed Forward Networks. Learning of ANN. Applications of ANN.

INTRODUCTION Neural networks are the simplified models of the

biological neuron systems. Neural networks are typically organized in layers.

Layers are made up of a number of interconnected 'nodes' .which contain an 'activation function'.

Patterns are presented to the network via the 'input layer', which communicates to one or more 'hidden layers' where the actual processing is done via a system of weighted 'connections'.

The hidden layers then link to an 'output layer' where the answer is output

ARTIFICIAL NEURAL NETWORKS

Inputs

Output

An artificial neural network is composed of many artificial neurons that are linked together according to a specific network architecture. The objective of the neural network is to transform the inputs into meaningful outputs.

MODEL OF ARTIFICIAL NEURON An appropriate model/simulation of the nervous system should be

able to produce similar responses and behaviours in artificial systems.

The nervous system is build by relatively simple units, the neurons, socopying their behaviour and functionality should be the solution.

MODEL OF ARTIFICIAL NEURONNeuron consists of three basic components weights, thresholds and a

single activation functionA set or connection link: each of which is characterized by a weight

or strength of its own wkj. Specifically, a signal xj at the input synapse „j‟ connected to neuron „k‟ is multiplied by the synaptic wkj

An adder: For summing the input signals,weighted by respective synaptic strengths of the neuron in a linear operation.

I w1x1

n

w2 x2 ....... wn xn

w i x ii 1

MODEL OF ARTIFICIAL NEURON

Threshold for a Neuron:-The total input for each neuron is the sum of the weighted inputs to the neuron minus its threshold value. This is then passed through the sigmoid function. The equation for the transition in a neuron is :

a = 1/(1 + exp(- x)) where x = ai wi - Qa is the activation for the neuron ai is the activation for neuron i wi is the weightQ is the threshold subtracted

MODEL OF ARTIFICIAL NEURON

Activation function: An activation function f performs a mathematical operation on the signal output. The most common activation functions are:- Linear Function,

- Threshold Function,- Sigmoidal (S shaped) function,

The activation functions are chosen depending upon the type of problem to be solved by the network.

MODEL OF ARTIFICIAL NEURONActivation Functions f – Types:- Sigmoidal Function (S-shape function):-The nonlinear curved S-shape function is called the sigmoid function.

This is most common type of activation used to construct the neural networks. It is mathematically well behaved, differentiable and strictly increasing function.

This is explained as≈ 0 for large -ve input values,1 for large +ve values, with a smooth transition between the two.α is slope parameter also called shape parameter symbol the λ is also used to represented this parameter.

1Y f (I) ,0 f (I ) 11 e1/(1 exp( I )),0 f (I ) 1

I

NEURAL NETWORK ARCHITECTURE

An artificial Neural Network is defined as a data processing system consisting of a large number of interconnected processing elements or artificial neurons.

There are three fundamentally different classes of neural networks. Those are.

1. Single layer feedforward Networks.2. Multilayer feedforward Networks.3. Recurrent Networks.

Here we have to discuss the single layer feed forward network.

SINGLE-LAYER FEED FORWARD NETWORK

- Input layer of source nodes that projects directlyonto an output layer of neurons.

- “Single-layer” referring to the output layer of computation nodes (neuron).

20 March 2013

SINGLE-LAYER FEED FORWARD NETWORK

The above figure is a single layer feed forward neural network. It consists an input layer to receive the inputs and an output layer to output the vectors.

The input layer consists of „n‟ neurons, and the output layer contains„m‟neurons .

The weight of synapse connecting ith input neuron the jth output neuron is Wij.

1

2

3

4

1

2

3

Ii1

Ii2Ii3

Iin

Oi2

Oi3

Oin

Oi1W11 Io1

W21

Io2

Iom

W31

Wn1

Yo1

Yo2

Yom

SINGLE-LAYER FEED FORWARD NETWORKHere the inputs of the input layer and the outputs of the output layer is given as

SoHence, the input to the output layer can be given as

Because

The block diagram of a single layer feed forward network.

Ioj W1 j I I1

1

n 1

W2 j I I 2 Wnj I IN

Iin

Ii1

I i 2..

I

m 1

o

Oom

......

Oo1

Oo 2

..

O

I Io m 1 m n n 1O IW T W TI

n 1 m 1I IOI

F(I,W)I O

LEARNING IN ANNLearning methods in neural networks can be broadly classified in three basic

types.- Supervised Learning- Unsupervised Learning- Reinforcement Learning

Supervised Learning:-

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 outputsErrors are then calculated, causing the system to adjust the

weights which control the network. Here a teacher is assume to be present during the learning

process.

LEARNING IN ANN

Unsupervised Learning:- Here the target output is not presented to the network, Because

thereis no teacher to present the described patterns.

So the system learns of its own by discovering and adapting

to structural features of the input patterns.Reinforcement Learning:- In this method, a teacher though available, does not present the

expected answer but only indicates if the computed output is correct or incorrect.

The information provided helps the network in its learning process.

Here a reward is given for correct answer computed and a penalty for a wrong answer.

APPLICATIONS OF NEURAL NETWORKS Character Recognition:- Neural networks can be used to

recognize handwritten characters. Image Compression:- Neural networks can receive and

process vast amounts of information at once, making them useful in image compression.

Stock Market Prediction:- Neural networks can examine a lot of information quickly and sort it all out, they can be used to predict stock prices.

Travelling Salesman Problem:- Neural networks can solve the traveling salesman problem, but only to a certain degree of approximation.

Security and Loan Applications:- With the acceptation of a neural network that will decide whether or not to grant a loan.

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