SlideShare a Scribd company logo

Supervised Learning

Download as PPT, PDF
B
butest

The document provides an overview of artificial neural networks and their learning capabilities. It discusses: - How biological neural networks in the brain inspired artificial neural networks - The basic structure of artificial neurons and how they are connected in a network - Single layer perceptrons and how they can be trained to learn simple tasks using supervised learning algorithms like the perceptron learning rule - Multilayer neural networks with one or more hidden layers that can learn more complex patterns using backpropagation to modify weights.

1 of 73
Downloaded 705 times
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
04/26/10 Intelligent Systems and Soft Computing Lecture 7 Artificial neural networks: Supervised learning Introduction, or how the brain works The neuron as a simple computing element The perceptron Multilayer neural networks Accelerated learning in multilayer neural networks The Hopfield network Bidirectional associative memories (BAM) Summary
04/26/10 Intelligent Systems and Soft Computing Introduction, or how the brain works Machine learning involves adaptive mechanisms that enable computers to learn from experience, learn by example and learn by analogy. Learning capabilities can improve the performance of an intelligent system over time. The most popular approaches to machine learning are artificial neural networks and genetic algorithms . This lecture is dedicated to neural networks.
04/26/10 Intelligent Systems and Soft Computing A neural network can be defined as a model of reasoning based on the human brain. The brain consists of a densely interconnected set of nerve cells, or basic information-processing units, called neurons . The human brain incorporates nearly 10 billion neurons and 60 trillion connections, synapses , between them. By using multiple neurons simultaneously, the brain can perform its functions much faster than the fastest computers in existence today.
04/26/10 Intelligent Systems and Soft Computing Each neuron has a very simple structure, but an army of such elements constitutes a tremendous processing power. A neuron consists of a cell body, soma , a number of fibers called dendrites , and a single long fiber called the axon .
04/26/10 Intelligent Systems and Soft Computing Biological neural network
04/26/10 Intelligent Systems and Soft Computing Our brain can be considered as a highly complex, non-linear and parallel information-processing system. Information is stored and processed in a neural network simultaneously throughout the whole network, rather than at specific locations. In other words, in neural networks, both data and its processing are global rather than local. Learning is a fundamental and essential characteristic of biological neural networks. The ease with which they can learn led to attempts to emulate a biological neural network in a computer.
04/26/10 Intelligent Systems and Soft Computing An artificial neural network consists of a number of very simple processors, also called neurons , which are analogous to the biological neurons in the brain. The neurons are connected by weighted links passing signals from one neuron to another. The output signal is transmitted through the neuron’s outgoing connection. The outgoing connection splits into a number of branches that transmit the same signal. The outgoing branches terminate at the incoming connections of other neurons in the network.
04/26/10 Intelligent Systems and Soft Computing Architecture of a typical artificial neural network I n p u t S i g n a l s O u t p u t S i g n a l s
04/26/10 Intelligent Systems and Soft Computing Analogy between biological and artificial neural networks
04/26/10 Intelligent Systems and Soft Computing The neuron as a simple computing element Diagram of a neuron
04/26/10 Intelligent Systems and Soft Computing The neuron computes the weighted sum of the input signals and compares the result with a threshold value ,  . If the net input is less than the threshold, the neuron output is –1. But if the net input is greater than or equal to the threshold, the neuron becomes activated and its output attains a value +1. The neuron uses the following transfer or activation function : This type of activation function is called a sign function .
04/26/10 Intelligent Systems and Soft Computing Activation functions of a neuron
04/26/10 Intelligent Systems and Soft Computing Can a single neuron learn a task? In 1958, Frank Rosenblatt introduced a training algorithm that provided the first procedure for training a simple ANN: a perceptron . The perceptron is the simplest form of a neural network. It consists of a single neuron with adjustable synaptic weights and a hard limiter .
04/26/10 Intelligent Systems and Soft Computing Single-layer two-input perceptron
04/26/10 Intelligent Systems and Soft Computing The Perceptron The operation of Rosenblatt’s perceptron is based on the McCulloch and Pitts neuron model . The model consists of a linear combiner followed by a hard limiter. The weighted sum of the inputs is applied to the hard limiter, which produces an output equal to +1 if its input is positive and  1 if it is negative.
04/26/10 Intelligent Systems and Soft Computing The aim of the perceptron is to classify inputs, x 1 , x 2 , . . ., x n , into one of two classes, say A 1 and A 2 . In the case of an elementary perceptron, the n- dimensional space is divided by a hyperplane into two decision regions. The hyperplane is defined by the linearly separable function :
04/26/10 Intelligent Systems and Soft Computing Linear separability in the perceptrons
04/26/10 Intelligent Systems and Soft Computing How does the perceptron learn its classification tasks? This is done by making small adjustments in the weights to reduce the difference between the actual and desired outputs of the perceptron. The initial weights are randomly assigned, usually in the range [  0.5, 0.5], and then updated to obtain the output consistent with the training examples.
04/26/10 Intelligent Systems and Soft Computing If at iteration p , the actual output is Y ( p ) and the desired output is Y d ( p ), then the error is given by: where p = 1, 2, 3, . . . Iteration p here refers to the p th training example presented to the perceptron. If the error, e ( p ), is positive, we need to increase perceptron output Y ( p ), but if it is negative, we need to decrease Y ( p ).
04/26/10 Intelligent Systems and Soft Computing where p = 1, 2, 3, . . .  is the learning rate , a positive constant less than unity. The perceptron learning rule was first proposed by Rosenblatt in 1960. Using this rule we can derive the perceptron training algorithm for classification tasks. The perceptron learning rule   
04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm Step 1 : Initialisation Set initial weights w 1 , w 2 ,…, w n and threshold  to random numbers in the range [  0.5, 0.5]. If the error, e ( p ), is positive, we need to increase perceptron output Y ( p ), but if it is negative, we need to decrease Y ( p ).
04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm (continued) Step 2 : Activation Activate the perceptron by applying inputs x 1 ( p ), x 2 ( p ),…, x n ( p ) and desired output Y d ( p ). Calculate the actual output at iteration p = 1 where n is the number of the perceptron inputs, and step is a step activation function.
04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm (continued) Step 3 : Weight training Update the weights of the perceptron where  w i ( p ) is the weight correction at iteration p . The weight correction is computed by the delta rule : Step 4 : Iteration Increase iteration p by one, go back to Step 2 and repeat the process until convergence. .
04/26/10 Intelligent Systems and Soft Computing Example of perceptron learning: the logical operation AND
04/26/10 Intelligent Systems and Soft Computing Two-dimensional plots of basic logical operations A perceptron can learn the operations AND and OR , but not Exclusive-OR . ( a ) AND ( x 1  x 2 )
04/26/10 Intelligent Systems and Soft Computing Multilayer neural networks A multilayer perceptron is a feedforward neural network with one or more hidden layers. The network consists of an input layer of source neurons, at least one middle or hidden layer of computational neurons, and an output layer of computational neurons. The input signals are propagated in a forward direction on a layer-by-layer basis.
04/26/10 Intelligent Systems and Soft Computing Multilayer perceptron with two hidden layers I n p u t S i g n a l s O u t p u t S i g n a l s
04/26/10 Intelligent Systems and Soft Computing What does the middle layer hide? A hidden layer “hides” its desired output. Neurons in the hidden layer cannot be observed through the input/output behavior of the network. There is no obvious way to know what the desired output of the hidden layer should be. Commercial ANNs incorporate three and sometimes four layers, including one or two hidden layers. Each layer can contain from 10 to 1000 neurons. Experimental neural networks may have five or even six layers, including three or four hidden layers, and utilize millions of neurons.
04/26/10 Intelligent Systems and Soft Computing Back-propagation neural network Learning in a multilayer network proceeds the same way as for a perceptron. A training set of input patterns is presented to the network. The network computes its output pattern, and if there is an error  or in other words a difference between actual and desired output patterns  the weights are adjusted to reduce this error.
04/26/10 Intelligent Systems and Soft Computing In a back-propagation neural network, the learning algorithm has two phases. First, a training input pattern is presented to the network input layer. The network propagates the input pattern from layer to layer until the output pattern is generated by the output layer. If this pattern is different from the desired output, an error is calculated and then propagated backwards through the network from the output layer to the input layer. The weights are modified as the error is propagated.
04/26/10 Intelligent Systems and Soft Computing Three-layer back-propagation neural network
04/26/10 Intelligent Systems and Soft Computing The back-propagation training algorithm Step 1 : Initialization Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range: where F i is the total number of inputs of neuron i in the network. The weight initialization is done on a neuron-by-neuron basis.
04/26/10 Intelligent Systems and Soft Computing Step 2 : Activation Activate the back-propagation neural network by applying inputs x 1 ( p ), x 2 ( p ),…, x n ( p ) and desired outputs y d ,1 ( p ), y d ,2 ( p ),…, y d , n ( p ). ( a ) Calculate the actual outputs of the neurons in the hidden layer: where n is the number of inputs of neuron j in the hidden layer, and sigmoid is the sigmoid activation function.
04/26/10 Intelligent Systems and Soft Computing ( b ) Calculate the actual outputs of the neurons in the output layer: Step 2 : Activation (continued) where m is the number of inputs of neuron k in the output layer.
04/26/10 Intelligent Systems and Soft Computing Step 3 : Weight training Update the weights in the back-propagation network propagating backward the errors associated with output neurons. ( a ) Calculate the error gradient for the neurons in the output layer: where Calculate the weight corrections: Update the weights at the output neurons:
04/26/10 Intelligent Systems and Soft Computing ( b ) Calculate the error gradient for the neurons in the hidden layer: Step 3 : Weight training (continued) Calculate the weight corrections: Update the weights at the hidden neurons:
04/26/10 Intelligent Systems and Soft Computing Step 4 : Iteration Increase iteration p by one, go back to Step 2 and repeat the process until the selected error criterion is satisfied. As an example, we may consider the three-layer back-propagation network. Suppose that the network is required to perform logical operation Exclusive-OR . Recall that a single-layer perceptron could not do this operation. Now we will apply the three-layer net.
04/26/10 Intelligent Systems and Soft Computing Three-layer network for solving the Exclusive-OR operation
04/26/10 Intelligent Systems and Soft Computing The effect of the threshold applied to a neuron in the hidden or output layer is represented by its weight,  , connected to a fixed input equal to  1. The initial weights and threshold levels are set randomly as follows: w 13 = 0.5, w 14 = 0.9, w 23 = 0.4, w 24 = 1.0, w 35 =  1.2, w 45 = 1.1,  3 = 0.8,  4 =  0.1 and  5 = 0.3.
04/26/10 Intelligent Systems and Soft Computing We consider a training set where inputs x 1 and x 2 are equal to 1 and desired output y d ,5 is 0. The actual outputs of neurons 3 and 4 in the hidden layer are calculated as Now the actual output of neuron 5 in the output layer is determined as: Thus, the following error is obtained:
04/26/10 Intelligent Systems and Soft Computing The next step is weight training. To update the weights and threshold levels in our network, we propagate the error, e , from the output layer backward to the input layer. First, we calculate the error gradient for neuron 5 in the output layer: Then we determine the weight corrections assuming that the learning rate parameter,  , is equal to 0.1:
04/26/10 Intelligent Systems and Soft Computing Next we calculate the error gradients for neurons 3 and 4 in the hidden layer: We then determine the weight corrections:
04/26/10 Intelligent Systems and Soft Computing At last, we update all weights and threshold: The training process is repeated until the sum of squared errors is less than 0.001.
04/26/10 Intelligent Systems and Soft Computing Learning curve for operation Exclusive-OR Sum-Squared Error
04/26/10 Intelligent Systems and Soft Computing Final results of three-layer network learning
04/26/10 Intelligent Systems and Soft Computing Network represented by McCulloch-Pitts model for solving the Exclusive-OR operation
04/26/10 Intelligent Systems and Soft Computing Decision boundaries Decision boundary constructed by hidden neuron 3; ( b ) Decision boundary constructed by hidden neuron 4; ( c ) Decision boundaries constructed by the complete three-layer network
04/26/10 Intelligent Systems and Soft Computing Accelerated learning in multilayer neural networks A multilayer network learns much faster when the sigmoidal activation function is represented by a hyperbolic tangent : where a and b are constants. Suitable values for a and b are: a = 1.716 and b = 0. 667
04/26/10 Intelligent Systems and Soft Computing We also can accelerate training by including a momentum term in the delta rule: where  is a positive number (0  1) called the momentum constant . Typically, the momentum constant is set to 0.95. This equation is called the generalised delta rule .
04/26/10 Intelligent Systems and Soft Computing Learning with momentum for operation Exclusive-OR Learning Rate
04/26/10 Intelligent Systems and Soft Computing Learning with adaptive learning rate To accelerate the convergence and yet avoid the danger of instability, we can apply two heuristics: Heuristic 1 If the change of the sum of squared errors has the same algebraic sign for several consequent epochs, then the learning rate parameter,  , should be increased. Heuristic 2 If the algebraic sign of the change of the sum of squared errors alternates for several consequent epochs, then the learning rate parameter,  , should be decreased.
04/26/10 Intelligent Systems and Soft Computing Adapting the learning rate requires some changes in the back-propagation algorithm. If the sum of squared errors at the current epoch exceeds the previous value by more than a predefined ratio (typically 1.04), the learning rate parameter is decreased (typically by multiplying by 0.7) and new weights and thresholds are calculated. If the error is less than the previous one, the learning rate is increased (typically by multiplying by 1.05).
04/26/10 Intelligent Systems and Soft Computing Learning with adaptive learning rate Sum-Squared Erro Learning Rate
04/26/10 Intelligent Systems and Soft Computing Learning with momentum and adaptive learning rate Sum-Squared Erro Learning Rate
04/26/10 Intelligent Systems and Soft Computing The Hopfield Network Neural networks were designed on analogy with the brain. The brain’s memory, however, works by association. For example, we can recognise a familiar face even in an unfamiliar environment within 100-200 ms. We can also recall a complete sensory experience, including sounds and scenes, when we hear only a few bars of music. The brain routinely associates one thing with another.
04/26/10 Intelligent Systems and Soft Computing Multilayer neural networks trained with the back-propagation algorithm are used for pattern recognition problems. However, to emulate the human memory’s associative characteristics we need a different type of network: a recurrent neural network . A recurrent neural network has feedback loops from its outputs to its inputs. The presence of such loops has a profound impact on the learning capability of the network.
04/26/10 Intelligent Systems and Soft Computing The stability of recurrent networks intrigued several researchers in the 1960s and 1970s. However, none was able to predict which network would be stable, and some researchers were pessimistic about finding a solution at all. The problem was solved only in 1982, when John Hopfield formulated the physical principle of storing information in a dynamically stable network.
04/26/10 Intelligent Systems and Soft Computing Single-layer n -neuron Hopfield network I n p u t S i g n a l s O u t p u t S i g n a l s
04/26/10 Intelligent Systems and Soft Computing The Hopfield network uses McCulloch and Pitts neurons with the sign activation function as its computing element:
04/26/10 Intelligent Systems and Soft Computing The current state of the Hopfield network is determined by the current outputs of all neurons, y 1 , y 2 , . . ., y n . Thus, for a single-layer n -neuron network, the state can be defined by the state vector as:
04/26/10 Intelligent Systems and Soft Computing In the Hopfield network, synaptic weights between neurons are usually represented in matrix form as follows: where M is the number of states to be memorised by the network, Y m is the n-dimensional binary vector, I is n  n identity matrix, and superscript T denotes matrix transposition.
04/26/10 Intelligent Systems and Soft Computing Possible states for the three-neuron Hopfield network
04/26/10 Intelligent Systems and Soft Computing The stable state-vertex is determined by the weight matrix W , the current input vector X , and the threshold matrix  . If the input vector is partially incorrect or incomplete, the initial state will converge into the stable state-vertex after a few iterations. Suppose, for instance, that our network is required to memorise two opposite states, (1, 1, 1) and (  1,  1,  1). Thus, where Y 1 and Y 2 are the three-dimensional vectors. or
04/26/10 Intelligent Systems and Soft Computing The 3  3 identity matrix I is Thus, we can now determine the weight matrix as follows: Next, the network is tested by the sequence of input vectors, X 1 and X 2 , which are equal to the output (or target) vectors Y 1 and Y 2 , respectively.
04/26/10 Intelligent Systems and Soft Computing First, we activate the Hopfield network by applying the input vector X . Then, we calculate the actual output vector Y , and finally, we compare the result with the initial input vector X .
04/26/10 Intelligent Systems and Soft Computing The remaining six states are all unstable. However, stable states (also called fundamental memories ) are capable of attracting states that are close to them. The fundamental memory (1, 1, 1) attracts unstable states (  1, 1, 1), (1,  1, 1) and (1, 1,  1). Each of these unstable states represents a single error, compared to the fundamental memory (1, 1, 1). The fundamental memory (  1,  1,  1) attracts unstable states (  1,  1, 1), (  1, 1,  1) and (1,  1,  1). Thus, the Hopfield network can act as an error correction network .
04/26/10 Intelligent Systems and Soft Computing Storage capacity of the Hopfield network Storage capacity is the largest number of fundamental memories that can be stored and retrieved correctly. The maximum number of fundamental memories M max that can be stored in the n -neuron recurrent network is limited by On the basis that most of the fundamental memories are to be retrived perfectly: M max =n/2ln n
04/26/10 Intelligent Systems and Soft Computing Bidirectional associative memory (BAM) The Hopfield network represents an autoassociative type of memory  it can retrieve a corrupted or incomplete memory but cannot associate this memory with another different memory. Human memory is essentially associative . One thing may remind us of another, and that of another, and so on. We use a chain of mental associations to recover a lost memory. If we forget where we left an umbrella, we try to recall where we last had it, what we were doing, and who we were talking to. We attempt to establish a chain of associations, and thereby to restore a lost memory.
04/26/10 Intelligent Systems and Soft Computing To associate one memory with another, we need a recurrent neural network capable of accepting an input pattern on one set of neurons and producing a related, but different, output pattern on another set of neurons. Bidirectional associative memory (BAM) , first proposed by Bart Kosko , is a heteroassociative network. It associates patterns from one set, set A , to patterns from another set, set B , and vice versa. Like a Hopfield network, the BAM can generalise and also produce correct outputs despite corrupted or incomplete inputs.
04/26/10 Intelligent Systems and Soft Computing BAM operation
04/26/10 Intelligent Systems and Soft Computing The basic idea behind the BAM is to store pattern pairs so that when n -dimensional vector X from set A is presented as input, the BAM recalls m -dimensional vector Y from set B , but when Y is presented as input, the BAM recalls X .
04/26/10 Intelligent Systems and Soft Computing To develop the BAM, we need to create a correlation matrix for each pattern pair we want to store. The correlation matrix is the matrix product of the input vector X , and the transpose of the output vector Y T . The BAM weight matrix is the sum of all correlation matrices, that is, where M is the number of pattern pairs to be stored in the BAM.
04/26/10 Intelligent Systems and Soft Computing Stability and storage capacity of the BAM The BAM is unconditionally stable . This means that any set of associations can be learned without risk of instability. The maximum number of associations to be stored in the BAM should not exceed the number of neurons in the smaller layer. The more serious problem with the BAM is incorrect convergence . The BAM may not always produce the closest association. In fact, a stable association may be only slightly related to the initial input vector.

More Related Content

What's hot (20)

PDF
Machine learning
Amit Kumar Rathi
 
DOCX
Learning Methods in a Neural Network
Saransh Choudhary
 
PPTX
Fuzzy rules and fuzzy reasoning
Veni7
 
PPSX
Perceptron (neural network)
EdutechLearners
 
PPT
2.5 backpropagation
Krish_ver2
 
PPTX
Activation functions
PRATEEK SAHU
 
PPT
Back propagation
Nagarajan
 
PDF
Artificial Neural Networks Lect3: Neural Network Learning rules
Mohammed Bennamoun
 
PPTX
Convolutional Neural Network and Its Applications
Kasun Chinthaka Piyarathna
 
PPTX
HOPFIELD NETWORK
ankita pandey
 
PPTX
Genetic algorithms vs Traditional algorithms
Dr. C.V. Suresh Babu
 
PDF
Foundations of Machine Learning
mahutte
 
PPTX
Defuzzification
Dr. C.V. Suresh Babu
 
PPT
backpropagation in neural networks
Akash Goel
 
PPTX
Analytical learning
swapnac12
 
PPTX
Multi Layer Network
International Islamic University
 
PPTX
Introduction to Genetic Algorithms
Dr. C.V. Suresh Babu
 
PPTX
08 clustering
นนทวัฒน์ บุญบา
 
PPT
E.s unit 6
Sneha Chopra
 
PDF
Artificial Neural Network Lect4 : Single Layer Perceptron Classifiers
Mohammed Bennamoun
 
Machine learning
Amit Kumar Rathi
 
Learning Methods in a Neural Network
Saransh Choudhary
 
Fuzzy rules and fuzzy reasoning
Veni7
 
Perceptron (neural network)
EdutechLearners
 
2.5 backpropagation
Krish_ver2
 
Activation functions
PRATEEK SAHU
 
Back propagation
Nagarajan
 
Artificial Neural Networks Lect3: Neural Network Learning rules
Mohammed Bennamoun
 
Convolutional Neural Network and Its Applications
Kasun Chinthaka Piyarathna
 
HOPFIELD NETWORK
ankita pandey
 
Genetic algorithms vs Traditional algorithms
Dr. C.V. Suresh Babu
 
Foundations of Machine Learning
mahutte
 
Defuzzification
Dr. C.V. Suresh Babu
 
backpropagation in neural networks
Akash Goel
 
Analytical learning
swapnac12
 
Multi Layer Network
International Islamic University
 
Introduction to Genetic Algorithms
Dr. C.V. Suresh Babu
 
08 clustering
นนทวัฒน์ บุญบา
 
E.s unit 6
Sneha Chopra
 
Artificial Neural Network Lect4 : Single Layer Perceptron Classifiers
Mohammed Bennamoun
 

Viewers also liked (6)

PPTX
Supervised and unsupervised learning
Paras Kohli
 
PPTX
supervised learning
Amar Tripathi
 
PPTX
A very easy explanation to understanding machine learning (Supervised & Unsup...
Ryo Onozuka
 
PPTX
Presentation on supervised learning
Tonmoy Bhagawati
 
PPTX
Introduction to Machine Learning
Lior Rokach
 
PPTX
Introduction to Machine Learning
Rahul Jain
 
Supervised and unsupervised learning
Paras Kohli
 
supervised learning
Amar Tripathi
 
A very easy explanation to understanding machine learning (Supervised & Unsup...
Ryo Onozuka
 
Presentation on supervised learning
Tonmoy Bhagawati
 
Introduction to Machine Learning
Lior Rokach
 
Introduction to Machine Learning
Rahul Jain
 
Ad

Similar to Supervised Learning (20)

PPT
lecture07.ppt
butest
 
PPS
Neural Networks Ver1
ncct
 
PPT
SOFT COMPUTERING TECHNICS -Unit 1
sravanthi computers
 
PPT
19_Learning.ppt
gnans Kgnanshek
 
PDF
10-Perceptron.pdf
ESTIBALYZJIMENEZCAST
 
PPT
Soft Computing-173101
AMIT KUMAR
 
PPT
AI-CH5 (ANN) - Artificial Neural Network
abrahadawit101
 
PPTX
Neural Networks For Secondary Structure.pptx
ssuser1774d3
 
PPT
ANN.ppt
UI19EC21Talluriissak
 
PDF
Deep Learning detailkesdSECA4002 doc.pdf
Gayatri Wahane
 
PPT
Artificial Neural Network and Machine Learning
vipulkondekar
 
PPT
Neural-Networks, images and examples details
mousmiin
 
PPT
Neural-Networks2Neural Network Classifier.ppt
dabeli2153
 
PPT
NeuralNetworksbasics for Deeplearning
TSANKARARAO
 
PPT
Neural-Networks full covering AI networks.ppt
cs18115
 
PPT
Neural network final NWU 4.3 Graphics Course
Mohaiminur Rahman
 
PPTX
Artificial neural networks: Supervised learning
jesawid181
 
PPT
Neuralnetwork 101222074552-phpapp02
Deepu Gupta
 
PDF
BACKPROPOGATION ALGO.pdfLECTURE NOTES WITH SOLVED EXAMPLE AND FEED FORWARD NE...
DurgadeviParamasivam
 
PDF
Artificial Neural Network-Types,Perceptron,Problems
Sharmila Chidaravalli
 
lecture07.ppt
butest
 
Neural Networks Ver1
ncct
 
SOFT COMPUTERING TECHNICS -Unit 1
sravanthi computers
 
19_Learning.ppt
gnans Kgnanshek
 
10-Perceptron.pdf
ESTIBALYZJIMENEZCAST
 
Soft Computing-173101
AMIT KUMAR
 
AI-CH5 (ANN) - Artificial Neural Network
abrahadawit101
 
Neural Networks For Secondary Structure.pptx
ssuser1774d3
 
ANN.ppt
UI19EC21Talluriissak
 
Deep Learning detailkesdSECA4002 doc.pdf
Gayatri Wahane
 
Artificial Neural Network and Machine Learning
vipulkondekar
 
Neural-Networks, images and examples details
mousmiin
 
Neural-Networks2Neural Network Classifier.ppt
dabeli2153
 
NeuralNetworksbasics for Deeplearning
TSANKARARAO
 
Neural-Networks full covering AI networks.ppt
cs18115
 
Neural network final NWU 4.3 Graphics Course
Mohaiminur Rahman
 
Artificial neural networks: Supervised learning
jesawid181
 
Neuralnetwork 101222074552-phpapp02
Deepu Gupta
 
BACKPROPOGATION ALGO.pdfLECTURE NOTES WITH SOLVED EXAMPLE AND FEED FORWARD NE...
DurgadeviParamasivam
 
Artificial Neural Network-Types,Perceptron,Problems
Sharmila Chidaravalli
 
Ad

More from butest (20)

PDF
EL MODELO DE NEGOCIO DE YOUTUBE
butest
 
DOC
1. MPEG I.B.P frame之不同
butest
 
PDF
LESSONS FROM THE MICHAEL JACKSON TRIAL
butest
 
PPT
Timeline: The Life of Michael Jackson
butest
 
DOCX
Popular Reading Last Updated April 1, 2010 Adams, Lorraine The ...
butest
 
PDF
LESSONS FROM THE MICHAEL JACKSON TRIAL
butest
 
PPTX
Com 380, Summer II
butest
 
PPT
PPT
butest
 
DOCX
The MYnstrel Free Press Volume 2: Economic Struggles, Meet Jazz
butest
 
DOC
MICHAEL JACKSON.doc
butest
 
PPTX
Social Networks: Twitter Facebook SL - Slide 1
butest
 
PPT
Facebook
butest
 
DOCX
Executive Summary Hare Chevrolet is a General Motors dealership ...
butest
 
DOC
Welcome to the Dougherty County Public Library's Facebook and ...
butest
 
DOC
NEWS ANNOUNCEMENT
butest
 
DOC
C-2100 Ultra Zoom.doc
butest
 
DOC
MAC Printing on ITS Printers.doc.doc
butest
 
DOC
Mac OS X Guide.doc
butest
 
DOC
hier
butest
 
DOC
WEB DESIGN!
butest
 
EL MODELO DE NEGOCIO DE YOUTUBE
butest
 
1. MPEG I.B.P frame之不同
butest
 
LESSONS FROM THE MICHAEL JACKSON TRIAL
butest
 
Timeline: The Life of Michael Jackson
butest
 
Popular Reading Last Updated April 1, 2010 Adams, Lorraine The ...
butest
 
LESSONS FROM THE MICHAEL JACKSON TRIAL
butest
 
Com 380, Summer II
butest
 
PPT
butest
 
The MYnstrel Free Press Volume 2: Economic Struggles, Meet Jazz
butest
 
MICHAEL JACKSON.doc
butest
 
Social Networks: Twitter Facebook SL - Slide 1
butest
 
Facebook
butest
 
Executive Summary Hare Chevrolet is a General Motors dealership ...
butest
 
Welcome to the Dougherty County Public Library's Facebook and ...
butest
 
NEWS ANNOUNCEMENT
butest
 
C-2100 Ultra Zoom.doc
butest
 
MAC Printing on ITS Printers.doc.doc
butest
 
Mac OS X Guide.doc
butest
 
hier
butest
 
WEB DESIGN!
butest
 

Supervised Learning

  • 1. 04/26/10 Intelligent Systems and Soft Computing Lecture 7 Artificial neural networks: Supervised learning Introduction, or how the brain works The neuron as a simple computing element The perceptron Multilayer neural networks Accelerated learning in multilayer neural networks The Hopfield network Bidirectional associative memories (BAM) Summary
  • 2. 04/26/10 Intelligent Systems and Soft Computing Introduction, or how the brain works Machine learning involves adaptive mechanisms that enable computers to learn from experience, learn by example and learn by analogy. Learning capabilities can improve the performance of an intelligent system over time. The most popular approaches to machine learning are artificial neural networks and genetic algorithms . This lecture is dedicated to neural networks.
  • 3. 04/26/10 Intelligent Systems and Soft Computing A neural network can be defined as a model of reasoning based on the human brain. The brain consists of a densely interconnected set of nerve cells, or basic information-processing units, called neurons . The human brain incorporates nearly 10 billion neurons and 60 trillion connections, synapses , between them. By using multiple neurons simultaneously, the brain can perform its functions much faster than the fastest computers in existence today.
  • 4. 04/26/10 Intelligent Systems and Soft Computing Each neuron has a very simple structure, but an army of such elements constitutes a tremendous processing power. A neuron consists of a cell body, soma , a number of fibers called dendrites , and a single long fiber called the axon .
  • 5. 04/26/10 Intelligent Systems and Soft Computing Biological neural network
  • 6. 04/26/10 Intelligent Systems and Soft Computing Our brain can be considered as a highly complex, non-linear and parallel information-processing system. Information is stored and processed in a neural network simultaneously throughout the whole network, rather than at specific locations. In other words, in neural networks, both data and its processing are global rather than local. Learning is a fundamental and essential characteristic of biological neural networks. The ease with which they can learn led to attempts to emulate a biological neural network in a computer.
  • 7. 04/26/10 Intelligent Systems and Soft Computing An artificial neural network consists of a number of very simple processors, also called neurons , which are analogous to the biological neurons in the brain. The neurons are connected by weighted links passing signals from one neuron to another. The output signal is transmitted through the neuron’s outgoing connection. The outgoing connection splits into a number of branches that transmit the same signal. The outgoing branches terminate at the incoming connections of other neurons in the network.
  • 8. 04/26/10 Intelligent Systems and Soft Computing Architecture of a typical artificial neural network I n p u t S i g n a l s O u t p u t S i g n a l s
  • 9. 04/26/10 Intelligent Systems and Soft Computing Analogy between biological and artificial neural networks
  • 10. 04/26/10 Intelligent Systems and Soft Computing The neuron as a simple computing element Diagram of a neuron
  • 11. 04/26/10 Intelligent Systems and Soft Computing The neuron computes the weighted sum of the input signals and compares the result with a threshold value ,  . If the net input is less than the threshold, the neuron output is –1. But if the net input is greater than or equal to the threshold, the neuron becomes activated and its output attains a value +1. The neuron uses the following transfer or activation function : This type of activation function is called a sign function .
  • 12. 04/26/10 Intelligent Systems and Soft Computing Activation functions of a neuron
  • 13. 04/26/10 Intelligent Systems and Soft Computing Can a single neuron learn a task? In 1958, Frank Rosenblatt introduced a training algorithm that provided the first procedure for training a simple ANN: a perceptron . The perceptron is the simplest form of a neural network. It consists of a single neuron with adjustable synaptic weights and a hard limiter .
  • 14. 04/26/10 Intelligent Systems and Soft Computing Single-layer two-input perceptron
  • 15. 04/26/10 Intelligent Systems and Soft Computing The Perceptron The operation of Rosenblatt’s perceptron is based on the McCulloch and Pitts neuron model . The model consists of a linear combiner followed by a hard limiter. The weighted sum of the inputs is applied to the hard limiter, which produces an output equal to +1 if its input is positive and  1 if it is negative.
  • 16. 04/26/10 Intelligent Systems and Soft Computing The aim of the perceptron is to classify inputs, x 1 , x 2 , . . ., x n , into one of two classes, say A 1 and A 2 . In the case of an elementary perceptron, the n- dimensional space is divided by a hyperplane into two decision regions. The hyperplane is defined by the linearly separable function :
  • 17. 04/26/10 Intelligent Systems and Soft Computing Linear separability in the perceptrons
  • 18. 04/26/10 Intelligent Systems and Soft Computing How does the perceptron learn its classification tasks? This is done by making small adjustments in the weights to reduce the difference between the actual and desired outputs of the perceptron. The initial weights are randomly assigned, usually in the range [  0.5, 0.5], and then updated to obtain the output consistent with the training examples.
  • 19. 04/26/10 Intelligent Systems and Soft Computing If at iteration p , the actual output is Y ( p ) and the desired output is Y d ( p ), then the error is given by: where p = 1, 2, 3, . . . Iteration p here refers to the p th training example presented to the perceptron. If the error, e ( p ), is positive, we need to increase perceptron output Y ( p ), but if it is negative, we need to decrease Y ( p ).
  • 20. 04/26/10 Intelligent Systems and Soft Computing where p = 1, 2, 3, . . .  is the learning rate , a positive constant less than unity. The perceptron learning rule was first proposed by Rosenblatt in 1960. Using this rule we can derive the perceptron training algorithm for classification tasks. The perceptron learning rule   
  • 21. 04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm Step 1 : Initialisation Set initial weights w 1 , w 2 ,…, w n and threshold  to random numbers in the range [  0.5, 0.5]. If the error, e ( p ), is positive, we need to increase perceptron output Y ( p ), but if it is negative, we need to decrease Y ( p ).
  • 22. 04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm (continued) Step 2 : Activation Activate the perceptron by applying inputs x 1 ( p ), x 2 ( p ),…, x n ( p ) and desired output Y d ( p ). Calculate the actual output at iteration p = 1 where n is the number of the perceptron inputs, and step is a step activation function.
  • 23. 04/26/10 Intelligent Systems and Soft Computing Perceptron’s training algorithm (continued) Step 3 : Weight training Update the weights of the perceptron where  w i ( p ) is the weight correction at iteration p . The weight correction is computed by the delta rule : Step 4 : Iteration Increase iteration p by one, go back to Step 2 and repeat the process until convergence. .
  • 24. 04/26/10 Intelligent Systems and Soft Computing Example of perceptron learning: the logical operation AND
  • 25. 04/26/10 Intelligent Systems and Soft Computing Two-dimensional plots of basic logical operations A perceptron can learn the operations AND and OR , but not Exclusive-OR . ( a ) AND ( x 1  x 2 )
  • 26. 04/26/10 Intelligent Systems and Soft Computing Multilayer neural networks A multilayer perceptron is a feedforward neural network with one or more hidden layers. The network consists of an input layer of source neurons, at least one middle or hidden layer of computational neurons, and an output layer of computational neurons. The input signals are propagated in a forward direction on a layer-by-layer basis.
  • 27. 04/26/10 Intelligent Systems and Soft Computing Multilayer perceptron with two hidden layers I n p u t S i g n a l s O u t p u t S i g n a l s
  • 28. 04/26/10 Intelligent Systems and Soft Computing What does the middle layer hide? A hidden layer “hides” its desired output. Neurons in the hidden layer cannot be observed through the input/output behavior of the network. There is no obvious way to know what the desired output of the hidden layer should be. Commercial ANNs incorporate three and sometimes four layers, including one or two hidden layers. Each layer can contain from 10 to 1000 neurons. Experimental neural networks may have five or even six layers, including three or four hidden layers, and utilize millions of neurons.
  • 29. 04/26/10 Intelligent Systems and Soft Computing Back-propagation neural network Learning in a multilayer network proceeds the same way as for a perceptron. A training set of input patterns is presented to the network. The network computes its output pattern, and if there is an error  or in other words a difference between actual and desired output patterns  the weights are adjusted to reduce this error.
  • 30. 04/26/10 Intelligent Systems and Soft Computing In a back-propagation neural network, the learning algorithm has two phases. First, a training input pattern is presented to the network input layer. The network propagates the input pattern from layer to layer until the output pattern is generated by the output layer. If this pattern is different from the desired output, an error is calculated and then propagated backwards through the network from the output layer to the input layer. The weights are modified as the error is propagated.
  • 31. 04/26/10 Intelligent Systems and Soft Computing Three-layer back-propagation neural network
  • 32. 04/26/10 Intelligent Systems and Soft Computing The back-propagation training algorithm Step 1 : Initialization Set all the weights and threshold levels of the network to random numbers uniformly distributed inside a small range: where F i is the total number of inputs of neuron i in the network. The weight initialization is done on a neuron-by-neuron basis.
  • 33. 04/26/10 Intelligent Systems and Soft Computing Step 2 : Activation Activate the back-propagation neural network by applying inputs x 1 ( p ), x 2 ( p ),…, x n ( p ) and desired outputs y d ,1 ( p ), y d ,2 ( p ),…, y d , n ( p ). ( a ) Calculate the actual outputs of the neurons in the hidden layer: where n is the number of inputs of neuron j in the hidden layer, and sigmoid is the sigmoid activation function.
  • 34. 04/26/10 Intelligent Systems and Soft Computing ( b ) Calculate the actual outputs of the neurons in the output layer: Step 2 : Activation (continued) where m is the number of inputs of neuron k in the output layer.
  • 35. 04/26/10 Intelligent Systems and Soft Computing Step 3 : Weight training Update the weights in the back-propagation network propagating backward the errors associated with output neurons. ( a ) Calculate the error gradient for the neurons in the output layer: where Calculate the weight corrections: Update the weights at the output neurons:
  • 36. 04/26/10 Intelligent Systems and Soft Computing ( b ) Calculate the error gradient for the neurons in the hidden layer: Step 3 : Weight training (continued) Calculate the weight corrections: Update the weights at the hidden neurons:
  • 37. 04/26/10 Intelligent Systems and Soft Computing Step 4 : Iteration Increase iteration p by one, go back to Step 2 and repeat the process until the selected error criterion is satisfied. As an example, we may consider the three-layer back-propagation network. Suppose that the network is required to perform logical operation Exclusive-OR . Recall that a single-layer perceptron could not do this operation. Now we will apply the three-layer net.
  • 38. 04/26/10 Intelligent Systems and Soft Computing Three-layer network for solving the Exclusive-OR operation
  • 39. 04/26/10 Intelligent Systems and Soft Computing The effect of the threshold applied to a neuron in the hidden or output layer is represented by its weight,  , connected to a fixed input equal to  1. The initial weights and threshold levels are set randomly as follows: w 13 = 0.5, w 14 = 0.9, w 23 = 0.4, w 24 = 1.0, w 35 =  1.2, w 45 = 1.1,  3 = 0.8,  4 =  0.1 and  5 = 0.3.
  • 40. 04/26/10 Intelligent Systems and Soft Computing We consider a training set where inputs x 1 and x 2 are equal to 1 and desired output y d ,5 is 0. The actual outputs of neurons 3 and 4 in the hidden layer are calculated as Now the actual output of neuron 5 in the output layer is determined as: Thus, the following error is obtained:
  • 41. 04/26/10 Intelligent Systems and Soft Computing The next step is weight training. To update the weights and threshold levels in our network, we propagate the error, e , from the output layer backward to the input layer. First, we calculate the error gradient for neuron 5 in the output layer: Then we determine the weight corrections assuming that the learning rate parameter,  , is equal to 0.1:
  • 42. 04/26/10 Intelligent Systems and Soft Computing Next we calculate the error gradients for neurons 3 and 4 in the hidden layer: We then determine the weight corrections:
  • 43. 04/26/10 Intelligent Systems and Soft Computing At last, we update all weights and threshold: The training process is repeated until the sum of squared errors is less than 0.001.
  • 44. 04/26/10 Intelligent Systems and Soft Computing Learning curve for operation Exclusive-OR Sum-Squared Error
  • 45. 04/26/10 Intelligent Systems and Soft Computing Final results of three-layer network learning
  • 46. 04/26/10 Intelligent Systems and Soft Computing Network represented by McCulloch-Pitts model for solving the Exclusive-OR operation
  • 47. 04/26/10 Intelligent Systems and Soft Computing Decision boundaries Decision boundary constructed by hidden neuron 3; ( b ) Decision boundary constructed by hidden neuron 4; ( c ) Decision boundaries constructed by the complete three-layer network
  • 48. 04/26/10 Intelligent Systems and Soft Computing Accelerated learning in multilayer neural networks A multilayer network learns much faster when the sigmoidal activation function is represented by a hyperbolic tangent : where a and b are constants. Suitable values for a and b are: a = 1.716 and b = 0. 667
  • 49. 04/26/10 Intelligent Systems and Soft Computing We also can accelerate training by including a momentum term in the delta rule: where  is a positive number (0  1) called the momentum constant . Typically, the momentum constant is set to 0.95. This equation is called the generalised delta rule .
  • 50. 04/26/10 Intelligent Systems and Soft Computing Learning with momentum for operation Exclusive-OR Learning Rate
  • 51. 04/26/10 Intelligent Systems and Soft Computing Learning with adaptive learning rate To accelerate the convergence and yet avoid the danger of instability, we can apply two heuristics: Heuristic 1 If the change of the sum of squared errors has the same algebraic sign for several consequent epochs, then the learning rate parameter,  , should be increased. Heuristic 2 If the algebraic sign of the change of the sum of squared errors alternates for several consequent epochs, then the learning rate parameter,  , should be decreased.
  • 52. 04/26/10 Intelligent Systems and Soft Computing Adapting the learning rate requires some changes in the back-propagation algorithm. If the sum of squared errors at the current epoch exceeds the previous value by more than a predefined ratio (typically 1.04), the learning rate parameter is decreased (typically by multiplying by 0.7) and new weights and thresholds are calculated. If the error is less than the previous one, the learning rate is increased (typically by multiplying by 1.05).
  • 53. 04/26/10 Intelligent Systems and Soft Computing Learning with adaptive learning rate Sum-Squared Erro Learning Rate
  • 54. 04/26/10 Intelligent Systems and Soft Computing Learning with momentum and adaptive learning rate Sum-Squared Erro Learning Rate
  • 55. 04/26/10 Intelligent Systems and Soft Computing The Hopfield Network Neural networks were designed on analogy with the brain. The brain’s memory, however, works by association. For example, we can recognise a familiar face even in an unfamiliar environment within 100-200 ms. We can also recall a complete sensory experience, including sounds and scenes, when we hear only a few bars of music. The brain routinely associates one thing with another.
  • 56. 04/26/10 Intelligent Systems and Soft Computing Multilayer neural networks trained with the back-propagation algorithm are used for pattern recognition problems. However, to emulate the human memory’s associative characteristics we need a different type of network: a recurrent neural network . A recurrent neural network has feedback loops from its outputs to its inputs. The presence of such loops has a profound impact on the learning capability of the network.
  • 57. 04/26/10 Intelligent Systems and Soft Computing The stability of recurrent networks intrigued several researchers in the 1960s and 1970s. However, none was able to predict which network would be stable, and some researchers were pessimistic about finding a solution at all. The problem was solved only in 1982, when John Hopfield formulated the physical principle of storing information in a dynamically stable network.
  • 58. 04/26/10 Intelligent Systems and Soft Computing Single-layer n -neuron Hopfield network I n p u t S i g n a l s O u t p u t S i g n a l s
  • 59. 04/26/10 Intelligent Systems and Soft Computing The Hopfield network uses McCulloch and Pitts neurons with the sign activation function as its computing element:
  • 60. 04/26/10 Intelligent Systems and Soft Computing The current state of the Hopfield network is determined by the current outputs of all neurons, y 1 , y 2 , . . ., y n . Thus, for a single-layer n -neuron network, the state can be defined by the state vector as:
  • 61. 04/26/10 Intelligent Systems and Soft Computing In the Hopfield network, synaptic weights between neurons are usually represented in matrix form as follows: where M is the number of states to be memorised by the network, Y m is the n-dimensional binary vector, I is n  n identity matrix, and superscript T denotes matrix transposition.
  • 62. 04/26/10 Intelligent Systems and Soft Computing Possible states for the three-neuron Hopfield network
  • 63. 04/26/10 Intelligent Systems and Soft Computing The stable state-vertex is determined by the weight matrix W , the current input vector X , and the threshold matrix  . If the input vector is partially incorrect or incomplete, the initial state will converge into the stable state-vertex after a few iterations. Suppose, for instance, that our network is required to memorise two opposite states, (1, 1, 1) and (  1,  1,  1). Thus, where Y 1 and Y 2 are the three-dimensional vectors. or
  • 64. 04/26/10 Intelligent Systems and Soft Computing The 3  3 identity matrix I is Thus, we can now determine the weight matrix as follows: Next, the network is tested by the sequence of input vectors, X 1 and X 2 , which are equal to the output (or target) vectors Y 1 and Y 2 , respectively.
  • 65. 04/26/10 Intelligent Systems and Soft Computing First, we activate the Hopfield network by applying the input vector X . Then, we calculate the actual output vector Y , and finally, we compare the result with the initial input vector X .
  • 66. 04/26/10 Intelligent Systems and Soft Computing The remaining six states are all unstable. However, stable states (also called fundamental memories ) are capable of attracting states that are close to them. The fundamental memory (1, 1, 1) attracts unstable states (  1, 1, 1), (1,  1, 1) and (1, 1,  1). Each of these unstable states represents a single error, compared to the fundamental memory (1, 1, 1). The fundamental memory (  1,  1,  1) attracts unstable states (  1,  1, 1), (  1, 1,  1) and (1,  1,  1). Thus, the Hopfield network can act as an error correction network .
  • 67. 04/26/10 Intelligent Systems and Soft Computing Storage capacity of the Hopfield network Storage capacity is the largest number of fundamental memories that can be stored and retrieved correctly. The maximum number of fundamental memories M max that can be stored in the n -neuron recurrent network is limited by On the basis that most of the fundamental memories are to be retrived perfectly: M max =n/2ln n
  • 68. 04/26/10 Intelligent Systems and Soft Computing Bidirectional associative memory (BAM) The Hopfield network represents an autoassociative type of memory  it can retrieve a corrupted or incomplete memory but cannot associate this memory with another different memory. Human memory is essentially associative . One thing may remind us of another, and that of another, and so on. We use a chain of mental associations to recover a lost memory. If we forget where we left an umbrella, we try to recall where we last had it, what we were doing, and who we were talking to. We attempt to establish a chain of associations, and thereby to restore a lost memory.
  • 69. 04/26/10 Intelligent Systems and Soft Computing To associate one memory with another, we need a recurrent neural network capable of accepting an input pattern on one set of neurons and producing a related, but different, output pattern on another set of neurons. Bidirectional associative memory (BAM) , first proposed by Bart Kosko , is a heteroassociative network. It associates patterns from one set, set A , to patterns from another set, set B , and vice versa. Like a Hopfield network, the BAM can generalise and also produce correct outputs despite corrupted or incomplete inputs.
  • 70. 04/26/10 Intelligent Systems and Soft Computing BAM operation
  • 71. 04/26/10 Intelligent Systems and Soft Computing The basic idea behind the BAM is to store pattern pairs so that when n -dimensional vector X from set A is presented as input, the BAM recalls m -dimensional vector Y from set B , but when Y is presented as input, the BAM recalls X .
  • 72. 04/26/10 Intelligent Systems and Soft Computing To develop the BAM, we need to create a correlation matrix for each pattern pair we want to store. The correlation matrix is the matrix product of the input vector X , and the transpose of the output vector Y T . The BAM weight matrix is the sum of all correlation matrices, that is, where M is the number of pattern pairs to be stored in the BAM.
  • 73. 04/26/10 Intelligent Systems and Soft Computing Stability and storage capacity of the BAM The BAM is unconditionally stable . This means that any set of associations can be learned without risk of instability. The maximum number of associations to be stored in the BAM should not exceed the number of neurons in the smaller layer. The more serious problem with the BAM is incorrect convergence . The BAM may not always produce the closest association. In fact, a stable association may be only slightly related to the initial input vector.

Editor's Notes