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BEE4333 Intelligent Control

Hamzah Ahmad

Ext: 6024/6130

Artificial Intelligence: Artificial Neural Network (ANN)

Copyright ofHamzah AhmadFKEE, UMP

Todays Lesson 4.1 Basic Concept 4.2 ANN Applications

LO1 : Able to understand the concept of Artificial Neural Network and its applications


Basic Concept ANN born from the demand of machine

learning; computer learns from experience, examples and analogy.

Simple concept : computer attempts to model the human brain.

Also known as parallel distributed processors. Why we need an intelligent processor or

computer to replace current technology? To decide intelligently and interact accordingly.


Human Brain; biological NN

SOMA

SOMA

Synapses; connection between neutrons

Dendrites;Received information

Axon;sends

information

NEURONPlasticity : Neurons heading to right answer are strengthen and for the wrong answer is weakened.

Learning from experience!


LearningIN

PU

T S

IGN

ALS

OU

TP

UT S

IGN

ALS

INPUT LAYER OUTPUT LAYERMIDDLE LAYER

ANN Architecture


Learning Synapses has their own weight to express the

importance of input. ANN learns through iterated adjustment from

synapses weight. Weight is adjusted to cope with the output

environment regarding about its network input/output behavior.

Each neutron computes its activation level based on the I/O numerical weights.

The output of a neuron might be the final solution or the input to other networks.


How to design ANN? Decide how many neurons to be used. How the connections between neurons are

constructed? How many layers needed? Which learning algorithm to be apply? Train the ANN by initialize the weight and

update the weights from training sets.


ANN characteristicsAdvantages: A neural network can perform tasks that a linear program can

not. When an element of the neural network fails, it can continue

without any problem by their parallel nature. A neural network learns and does not need to be

reprogrammed. It can be implemented in any application. It can be implemented without any problem.

Disadvantages: The neural network needs training to operate. The architecture of a neural network is different from the

architecture of microprocessors therefore needs to be emulated. Requires high processing time for large neural networks.


Todays Lesson 4.3 ANN Model 4.4 ANN Learning 4.5 Simple ANN

LO1 : Able to understand basic concept of biases, thresholds and linear separability

LO2 : Able to analyze simple ANN (Perceptrons)


Examples of ANN


CategorizationFeedforward All signals flow in one direction only, i.e. from

lower layers (input) to upper layers (output)Feedback Signals from neurons in upper layers are fed

back to either its own or to neurons in lower layers.Cellular Connected in a cellular manner.


Exercise Construct 4 artificial neurons

2 neurons on the input and 2 neurons on the output Each arrow has its own weight. Those weight is multiplied to each value going through each

arrow - what this process define? If there is only ONE (1) input and a weight, so the output will be

the multiplication of both. For more than ONE (1) input and weights, then the neuron will sum up the values.

Consider the weight is ONE (1) for each arrow and set the input to be (0,0), (0,1), (1,1), (1,-1), (-1,1).

What happens? Change the weight randomly and differently between -0.5 to

0.5 to each arrows. What happens? Try changing the weight again other than above weights. Observed what happen.


ANN Learning In all of the neural paradigms, the application

of an ANN involves two phases:

(1) Learning phase (pengajaran) (2) Recall phase (penggunaan)

In the learning phase (usually offline) the ANN is trained until it has learned its tasks (through the adaptation of its weights)

The recall phase is used to solve the task.


ANN Learning An ANN solves a task when its weights are adapted

through a learning phase. All neural networks have to be trained before they

can be used. They are given training patterns and their weights are

adjusted iteratively until an error function is minimized.

Once the ANN has been trained no more training is needed.

Two types of learning prevailed in ANNs: Supervised learning:- learning with teacher signals or

targets Unsupervised learning:- learning without the use of

teacher signals


Supervised Learning In supervised learning the training patterns are provided

to the ANN together with a teaching signal or target. The difference between the ANN output and the target is

the error signal. Initially the output of the ANN gives a large error during

the learning phase. The error is then minimized through continuous

adaptation of the weights to solve the problem through a learning algorithm.

In the end when the error becomes very small, the ANN is assumed to have learned the task and training is stopped.

It can then be used to solve the task in the recall phase.


Supervised Learning

Matching the I/O pattern


Unsupervised Learning In unsupervised learning, the ANN is trained without

teaching signals or targets. It is only supplied with examples of the input patterns

that it will solve eventually. The ANN usually has an auxilliary cost function which

needs to be minimized like an energy function, distance, etc.

Usually a neuron is designated as a “winner” from similarities in the input patterns through competition.

The weights of the ANN are modified where a cost function is minimized.

At the end of the learning phase, the weights would have been adapted in such a manner such that similar patterns are clustered into a particular node.


ANN paradigm There are a number of ANN paradigms developed over

the past few decades. These ANN paradigms are mainly distinguished

through their different learning algorithms rather than their models.

Some ANN paradigms are named after their proposer such as Hopfield, Kohonen, etc.

Most ANNs are named after their learning algorithm such as Backpropagation, Competitive learning, Counter propagation, ART, etc. and some are named after their model such as BAM,

Basically a particular ANN can be divided into either a feedforward or a feedback model and into either a supervised or unsupervised learning mode.


ANN Classifications


ANN Performance The performance of an ANN is described by

the figure of merit, which expresses the number of recalled patterns when input patterns are applied, that could be complete, partially complete, or even noisy.

A 100% performance in recalled patterns means that for every trained input stimulus signal, the ANN always produces the desired output pattern.


ANN Performance


Basis of ANN computing idea Neuron computes the input signals and compares

the result with a threshold value, θ. If the input is less than θ, then the neuron output

is -1, otherwise +1. Hence, the following activation function(sign

function) is used,

where X is the net weighted input to neuron, xi is the i input value, wi is the weight of input i . n is the number of neuron input and Y is the neuron output.

𝑋=∑𝑖=1

𝑛

𝑥 𝑖𝑤𝑖𝑌={+1𝑖𝑓 𝑋 ≥𝜃

−1 𝑖𝑓 𝑋<𝜃 } 𝑌=𝑠𝑖𝑔𝑛[¿∑𝑖=1

𝑛

𝑥 𝑖𝑤 𝑖 −𝜃]


Other types of activation function

Y

X

+1

-1

0

Y

X

+1

-1

0

Y

X

+1

-1

0

Y

X

+1

-1

0

Stepfunction

Signfunction

Sigmoidfunction

Linearfunction

𝑌 𝑠𝑖𝑔𝑛={+1, 𝑖𝑓 𝑋≥ 0−1 , 𝑖𝑓 𝑋<0}

𝑌 𝑠𝑡𝑒𝑝={+1 ,𝑖𝑓 𝑋 ≥ 00 ,𝑖𝑓 𝑋<0 } 𝑌 𝑠𝑖𝑔𝑚𝑜𝑖𝑑=

1

1+𝑒−𝑋

X


Simple ANN: A Perceptron

Perceptron is used to classify input in two classes; e.g class A1 or A2.

A linear separable function is used to divide the n-dimensional space as follows;

Say, 2 inputs, then we have a characteristics as shown on left figure. θ is used to shift the bound.

Three dimensional states is also possible to be view.

∑𝑖=1

𝑛

𝑥 𝑖𝑤𝑖−𝜃=0

x2

x10

2

1


Simple Perceptron

Inputs

Output/bias

∑

x1

x2

w1

w2

θ

Hardlimiter

Threshold

LinearCombiner

Must be boolean!


Different training pattern based on weights defined

• Note that p1 and p2 are incorrectly being determined• p1 target is t=1 and p2 target is t=-1

Decisionboundary


Learning: Classification Learning is done by adjusting the actual output Y

to meet the desired output Yd. Usually, the initial weight is adjust between -0.5

to 0.5. At iteration k of the training example, we have the error e as

If the error is positive, the weight must be decrease and otherwise must be increase.

Perceptron learning rule also can be obtained where

α is the learning rate and 0< α<1.

𝑒 (𝑘)=𝑌 𝑑(𝑘)−𝑌 (𝑘)

𝑤𝑖 (𝑘+1 )=𝑤𝑖 (𝑘 )+∝×𝑥 𝑖(𝑘)×𝑒(𝑘)


Training algorithm

Step 1: Initialization Set initial weight wi between [-0.5,0.5]and θ.

Step 2: Activation Perceptron activation at iteration 1 for each input and a

specific Yd. e.g for a step activation function we have

Step 3: Weight training Perceptron weight is updated by

where = α X xi(p) X e(p)

Step 4: Iteration Next iteration at time k+1 and go to step 2 again.


Example Consider truth table of AND operation

How ANN of a single perceptron can be trained?

Consider a step activation function in this example.

Input x1 Input x2 AND (x1 ∩ x2)

0 0 0

0 1 0

1 0 0

1 1 1

Threshold, θ = 0.2Learning rate,α = 0.1

Use initial weight as 0.3 for x1 and -0.1 for x2

Epoch

Input x1

Input x2

Desired output

yd

Initial weight w1

Initial weight w2

Actual Outpu

t Y

Error, e

Final weight w1

Final weight w2

1 0 0 0 0.3 -0.1 0 0 0.3 -0.1

0 1 0 0.3 -0.1 0 0 0.3 -0.1

1 0 0 0.3 -0.1 1 -1 0.2 -0.1

1 1 1 0.2 -0.1 0 1 0.3 0.0

𝑌 (𝑝)=𝑠𝑡𝑒𝑝[∑𝑖=1

𝑛

𝑥 𝑖 (𝑝 )𝑤 𝑖 (𝑝) −𝜃]where = α x xi(p) x e(p)

The epoch continues until the weights are converging to a steady state values.


Now consider this problem Design a mobile robot that avoid collisions

using ANN. There are three inputs; right wheel velocity,

left wheel velocity and relative distance between robot and obstacle.

The output will be the mobile robot heading angle.

Write only two epoch for this problem.


Today Lessons 4.3 ANN Model 4.4 ANN Learning 4.5 Simple ANN


LO2 : Able to analyze simple ANN (Perceptrons)


Today Lessons 4.6 Multilayer Neural Networks &

Backpropagation Algorithm



Sigmoid function characteristics The sigmoid activation function with different values c. When c is large, the sigmoid becomes like a threshold

function and when is c small, the sigmoid becomes more like a straight line (linear).

When c is large learning is much faster but a lot of information is lost, however when c is small, learning is very slow but information is retained.

Because this function is differentiable, it enables the B.P. algorithm to adapt the lower layers of weights in a multilayer neural network.

Because this function is differentiable, it enables the B.P. algorithm to adapt the lower layers of weights in a multilayer neural network.


Multilayer neural networks Multilayer NN-feedforward neural network with

one or more hidden layer. Model consists of input layer, middle or hidden

layer and an output layer. Why hidden layer is important?

Input layer only receives input signal Output layer only display the output patterns. Hidden layer process the input signals; weight

represents feature of inputs.


Multilayer NN model

x1

x2

Inputs

x3

1st hidden layer

2nd hidden layer

Output


Multilayer Neural Network learning Multilayer NN learns through a learning

algorithm; the popular one is BACK-PROPAGATION.

The computations are similar to a simple perceptron.

Back-propagation has two phases; Input layer demonstrates the training input

pattern and then propagates from layer to layer to output.

The calculation for error will notify the system to modified the weights appropriately.


Back-propagation Each neurons must be connected to each

other. Calculations

Same as a simple perceptron case.

Typically, sigmoid function is used in Multilayer NN.


Back-propagation: Learning mode

Before the BP can be used, it requires target patterns or signals as it a supervised learning algorithm.

Training patterns are obtained from the samples of the types of inputs to be given to the multilayer neural network and their answers are identified by the researcher.

Examples of training patterns are samples of handwritten characters, process data, etc. following the tasks to be solved.

The configuration for training a neural network using the BP algorithm is shown in the figure below in which the training is done offline.

The objective is to minimize the error between the target and actual output and to find ∆w.


BP: Learning mode The error is calculated at every iteration and

is backpropagated through the layers of the ANN to adapt the weights.

The weights are adapted such that the error is minimized.

Once the error has reached a justified minimum value, the training is stopped, and the neural network is reconfigured in the recall mode to solve the task.


Error gradient


Let’s look for a specific case

i j kinputs output

xiyi

Error signals

Input signals

lmn

wij wjk


Understand more, learns more Error propagation starts from output layer

back to hidden layer. How to calculate error signals at layer k? How about calculation to update the weights

at layer k? Weight correction; or In sigmoid function, where


Weight correction in hidden layer

We use the same technique to find the weight in hidden layer.


Steps for calculations Step 1 : Initialization

Set weights and threshold randomly within a small range

Step 2 : Activation Use sigmoid activation function at hidden layer

and output layer Hidden layer;

Output layer;


Step for calculations Step 3 : Weight training

Calculating error gradient in output layer

where

Update ; Calculating error gradient in hidden layer

Update ;

Step 4 : Iteration Back to step 2 and repeat process until selected error

criterion is satisfied.


When does the training process stop?

Training process stop until the sum of squared error for the output y is less than a prescribed value; 0.001.

Sum of squared error : performance indicator of the system.

The smaller, the better the system performance.


More about back-propagation Different initial weights and threshold may

have different solutions, but finally the system has almost similar solutions.

The decisions boundaries can be view if we use the sign activation function.

Drawbacks of back-propagation Not suitable for biological neurons; to adjust the

neurons weight. Computational expensive Slower training


Consider other technique

Sigmoid function; f(x) = (1+e-x)-1

f(x) = xThe error signals are as follows.

δk = Lk (1- Lk )( tk - Lk )δj = Lj (1- Lj ) ∑k δk wkj

Adaptions of weights are defined as below.∆wkj( t + 1) = η δk Lj + α∆wkj( t )∆wji( t + 1) = η δj Li + α∆wji( t )


XOR PROBLEM


In this example, θ is not available!


∆Wji(t+1) = 0.1 X (-0.0035) X 0 + (0.9 X 0) = 0Wj01(t+1) = 0.55 + (0) = 0.55

Wj02(t+1) = 0.15 + (0) = 0.15


Examples

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