Radial Basis Function
MadhawaKasun
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19 slides
Jan 30, 2014
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About This Presentation
Radial Basis Function Neural Network Implementation using MATLAB
Slide Content
CSC 367 2.0 Mathematical Computing
Assignment 3
Radial Basis Functions
AS2010377
M.K.H.Gunasekara
Special Part 1
Department of Computer Science
UNIVERSITY OF SRI JAYEWARDENEPURA
Assignment 3
Radial Basis Functions
AS2010377
M.K.H.Gunasekara
Special Part 1
Department of Computer Science
UNIVERSITY OF SRI JAYEWARDENEPURA
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
1 | P a g e
Table of Contents
-
Introduction ............................................................................................................................................ 2
Methodology ........................................................................................................................................... 3
Implementation ...................................................................................................................................... 5
Results ..................................................................................................................................................... 6
Discussion.............................................................................................................................................. 10
Appendices ............................................................................................................................................ 11
1 | P a g e
Table of Contents
-
Introduction ............................................................................................................................................ 2
Methodology ........................................................................................................................................... 3
Implementation ...................................................................................................................................... 5
Results ..................................................................................................................................................... 6
Discussion.............................................................................................................................................. 10
Appendices ............................................................................................................................................ 11
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
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Introduction
Neural Networks offer a powerful framework for representing nonlinear mappings from
several inputs to one or more outputs.
An important application of neural networks is regression. Instead of mapping the inputs
into a discrete class label, the neural network maps the input variables into continuous
values. A major class of neural networks is the radial basis function (RBF) neural network.
We will look at the architecture of RBF neural networks, followed by its applications in both
regression and classification.
In this report Radial Basis function is discussed for clustering as unsupervised learning
algorithm. Radial basis function is simulated to cluster three flowers in a given data set
which is available in http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data.
2 | P a g e
Introduction
Neural Networks offer a powerful framework for representing nonlinear mappings from
several inputs to one or more outputs.
An important application of neural networks is regression. Instead of mapping the inputs
into a discrete class label, the neural network maps the input variables into continuous
values. A major class of neural networks is the radial basis function (RBF) neural network.
We will look at the architecture of RBF neural networks, followed by its applications in both
regression and classification.
In this report Radial Basis function is discussed for clustering as unsupervised learning
algorithm. Radial basis function is simulated to cluster three flowers in a given data set
which is available in http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data.
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
3 | P a g e
Methodology
Radial Basis Function
Figure 01 : One hidden layer with Radial Basis Activation Functions
Radial basis function (RBF) networks typically have three layers
1. Input Layer
2. A hidden layer with a non-linear RBF activation function
3. Output Layer
Where N is the number of neurons in the hidden layer,
is the center vector for neuron i, and
is
the weight of neuron i in the linear output neuron. Functions that depend only on the distance from
a center vector are radially symmetric about that vector, hence the name radial basis function. In the
basic form all inputs are connected to each hidden neuron. The norm is typically taken to be the
Euclidean distance and the radial basis function is commonly taken to be Gaussian Function
( )
(
‖ ‖
)
------ (1)
There are some other Radial Basis functions
Logistic Basis Function
( )
(
)
Multi-quadratics
( )
√
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Methodology
Radial Basis Function
Figure 01 : One hidden layer with Radial Basis Activation Functions
Radial basis function (RBF) networks typically have three layers
1. Input Layer
2. A hidden layer with a non-linear RBF activation function
3. Output Layer
Where N is the number of neurons in the hidden layer,
is the center vector for neuron i, and
is
the weight of neuron i in the linear output neuron. Functions that depend only on the distance from
a center vector are radially symmetric about that vector, hence the name radial basis function. In the
basic form all inputs are connected to each hidden neuron. The norm is typically taken to be the
Euclidean distance and the radial basis function is commonly taken to be Gaussian Function
( )
(
‖ ‖
)
------ (1)
There are some other Radial Basis functions
Logistic Basis Function
( )
(
)
Multi-quadratics
( )
√
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
4 | P a g e
Input nodes connected by weights to a set of RBF neurons fire proportionately to the distance
between the input and the neuron in the weight space
The activation of these nodes is used as inputs to the second layer. The second layer (output layer) is
treated as a simple Perceptron network
Training the RBF Network
This can be done positioning the RBF nodes and using the activation of RBF nodes to train the linear
outputs.
Positioning RBF nodes can be done in two ways; First method is randomly picking some of the data
points to act as basis functions. And the second method is trying to position the nodes so that they
are representative of typical inputs, like using k-means clustering algorithm.
In Activation function there is standard deviation parameter.
One option is, giving all nodes the same size, and testing lots of different sizes using a validation set
to select one that works. Alternatively we can select the size of RBF nodes so that the whole space is
coved by the receptive fields. So the width of the Gaussian should be set according to the maximum
distance between the locations of the hidden nodes (d), and the number of hidden nodes (M)
√
------ (2)
We can use this normalized Gaussian function also.
( )
(
‖ ‖
)
∑
(
‖
‖
)
------ (3)
Outputs of the RBF Network:
(
‖ ‖
)
Training the Perceptron Network
We can train Pereceptron Network by using supervised learning method. Therefore we train the
MLP Network according to targets.
4 | P a g e
Input nodes connected by weights to a set of RBF neurons fire proportionately to the distance
between the input and the neuron in the weight space
The activation of these nodes is used as inputs to the second layer. The second layer (output layer) is
treated as a simple Perceptron network
Training the RBF Network
This can be done positioning the RBF nodes and using the activation of RBF nodes to train the linear
outputs.
Positioning RBF nodes can be done in two ways; First method is randomly picking some of the data
points to act as basis functions. And the second method is trying to position the nodes so that they
are representative of typical inputs, like using k-means clustering algorithm.
In Activation function there is standard deviation parameter.
One option is, giving all nodes the same size, and testing lots of different sizes using a validation set
to select one that works. Alternatively we can select the size of RBF nodes so that the whole space is
coved by the receptive fields. So the width of the Gaussian should be set according to the maximum
distance between the locations of the hidden nodes (d), and the number of hidden nodes (M)
√
------ (2)
We can use this normalized Gaussian function also.
( )
(
‖ ‖
)
∑
(
‖
‖
)
------ (3)
Outputs of the RBF Network:
(
‖ ‖
)
Training the Perceptron Network
We can train Pereceptron Network by using supervised learning method. Therefore we train the
MLP Network according to targets.
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
5 | P a g e
Implementation
Implementation was done using MATLAB 7.10 (2010). Implementation was done according to
following methods
1. Locate RBF nodes into centers
2. Calculate for the Gaussian function
3. Calculate outputs of the RBF layer – Unsupervised Training
4. Make Perceptron Network for second layer –( I used MLP network without a hidden layer)
5. Train MLP Network according to targets and inputs (inputs are the output of RBF network) –
Supervised Training
6. Simulate the network
I have implement RBF Network with different strategies to compare the results
Using Randomly selected centers
Using K-Means Cluster centers
Using Non-normalized Gaussian function
Using Normalized Gaussian function
Using SVM for second layer
5 | P a g e
Implementation
Implementation was done using MATLAB 7.10 (2010). Implementation was done according to
following methods
1. Locate RBF nodes into centers
2. Calculate for the Gaussian function
3. Calculate outputs of the RBF layer – Unsupervised Training
4. Make Perceptron Network for second layer –( I used MLP network without a hidden layer)
5. Train MLP Network according to targets and inputs (inputs are the output of RBF network) –
Supervised Training
6. Simulate the network
I have implement RBF Network with different strategies to compare the results
Using Randomly selected centers
Using K-Means Cluster centers
Using Non-normalized Gaussian function
Using Normalized Gaussian function
Using SVM for second layer
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
6 | P a g e
Results
sepal length sepal width petal length petal width Expected Target Actual Output
5.1 3.5 1.4 0.2 Iris-setosa Iris-setosa
4.9 3 1.4 0.2 Iris-setosa Iris-setosa
4.7 3.2 1.3 0.2 Iris-setosa Iris-setosa
4.6 3.1 1.5 0.2 Iris-setosa Iris-setosa
5 3.6 1.4 0.2 Iris-setosa Iris-setosa
5.4 3.9 1.7 0.4 Iris-setosa Iris-setosa
4.6 3.4 1.4 0.3 Iris-setosa Iris-setosa
5 3.4 1.5 0.2 Iris-setosa Iris-setosa
4.4 2.9 1.4 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
5.4 3.7 1.5 0.2 Iris-setosa Iris-setosa
4.8 3.4 1.6 0.2 Iris-setosa Iris-setosa
4.8 3 1.4 0.1 Iris-setosa Iris-setosa
4.3 3 1.1 0.1 Iris-setosa Iris-setosa
5.8 4 1.2 0.2 Iris-setosa Iris-setosa
5.7 4.4 1.5 0.4 Iris-setosa Iris-setosa
5.4 3.9 1.3 0.4 Iris-setosa Iris-setosa
5.1 3.5 1.4 0.3 Iris-setosa Iris-setosa
5.7 3.8 1.7 0.3 Iris-setosa Iris-setosa
5.1 3.8 1.5 0.3 Iris-setosa Iris-setosa
5.4 3.4 1.7 0.2 Iris-setosa Iris-setosa
5.1 3.7 1.5 0.4 Iris-setosa Iris-setosa
4.6 3.6 1 0.2 Iris-setosa Iris-setosa
5.1 3.3 1.7 0.5 Iris-setosa Iris-setosa
4.8 3.4 1.9 0.2 Iris-setosa Iris-setosa
5 3 1.6 0.2 Iris-setosa Iris-setosa
5 3.4 1.6 0.4 Iris-setosa Iris-setosa
5.2 3.5 1.5 0.2 Iris-setosa Iris-setosa
5.2 3.4 1.4 0.2 Iris-setosa Iris-setosa
4.7 3.2 1.6 0.2 Iris-setosa Iris-setosa
4.8 3.1 1.6 0.2 Iris-setosa Iris-setosa
5.4 3.4 1.5 0.4 Iris-setosa Iris-setosa
5.2 4.1 1.5 0.1 Iris-setosa Iris-setosa
5.5 4.2 1.4 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
5 3.2 1.2 0.2 Iris-setosa Iris-setosa
5.5 3.5 1.3 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
6 | P a g e
Results
sepal length sepal width petal length petal width Expected Target Actual Output
5.1 3.5 1.4 0.2 Iris-setosa Iris-setosa
4.9 3 1.4 0.2 Iris-setosa Iris-setosa
4.7 3.2 1.3 0.2 Iris-setosa Iris-setosa
4.6 3.1 1.5 0.2 Iris-setosa Iris-setosa
5 3.6 1.4 0.2 Iris-setosa Iris-setosa
5.4 3.9 1.7 0.4 Iris-setosa Iris-setosa
4.6 3.4 1.4 0.3 Iris-setosa Iris-setosa
5 3.4 1.5 0.2 Iris-setosa Iris-setosa
4.4 2.9 1.4 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
5.4 3.7 1.5 0.2 Iris-setosa Iris-setosa
4.8 3.4 1.6 0.2 Iris-setosa Iris-setosa
4.8 3 1.4 0.1 Iris-setosa Iris-setosa
4.3 3 1.1 0.1 Iris-setosa Iris-setosa
5.8 4 1.2 0.2 Iris-setosa Iris-setosa
5.7 4.4 1.5 0.4 Iris-setosa Iris-setosa
5.4 3.9 1.3 0.4 Iris-setosa Iris-setosa
5.1 3.5 1.4 0.3 Iris-setosa Iris-setosa
5.7 3.8 1.7 0.3 Iris-setosa Iris-setosa
5.1 3.8 1.5 0.3 Iris-setosa Iris-setosa
5.4 3.4 1.7 0.2 Iris-setosa Iris-setosa
5.1 3.7 1.5 0.4 Iris-setosa Iris-setosa
4.6 3.6 1 0.2 Iris-setosa Iris-setosa
5.1 3.3 1.7 0.5 Iris-setosa Iris-setosa
4.8 3.4 1.9 0.2 Iris-setosa Iris-setosa
5 3 1.6 0.2 Iris-setosa Iris-setosa
5 3.4 1.6 0.4 Iris-setosa Iris-setosa
5.2 3.5 1.5 0.2 Iris-setosa Iris-setosa
5.2 3.4 1.4 0.2 Iris-setosa Iris-setosa
4.7 3.2 1.6 0.2 Iris-setosa Iris-setosa
4.8 3.1 1.6 0.2 Iris-setosa Iris-setosa
5.4 3.4 1.5 0.4 Iris-setosa Iris-setosa
5.2 4.1 1.5 0.1 Iris-setosa Iris-setosa
5.5 4.2 1.4 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
5 3.2 1.2 0.2 Iris-setosa Iris-setosa
5.5 3.5 1.3 0.2 Iris-setosa Iris-setosa
4.9 3.1 1.5 0.1 Iris-setosa Iris-setosa
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
7 | P a g e
4.4 3 1.3 0.2 Iris-setosa Iris-setosa
5.1 3.4 1.5 0.2 Iris-setosa Iris-setosa
5 3.5 1.3 0.3 Iris-setosa Iris-setosa
4.5 2.3 1.3 0.3 Iris-setosa Iris-setosa
4.4 3.2 1.3 0.2 Iris-setosa Iris-setosa
5 3.5 1.6 0.6 Iris-setosa Iris-setosa
5.1 3.8 1.9 0.4 Iris-setosa Iris-setosa
4.8 3 1.4 0.3 Iris-setosa Iris-setosa
5.1 3.8 1.6 0.2 Iris-setosa Iris-setosa
4.6 3.2 1.4 0.2 Iris-setosa Iris-setosa
5.3 3.7 1.5 0.2 Iris-setosa Iris-setosa
5 3.3 1.4 0.2 Iris-setosa Iris-setosa
7 3.2 4.7 1.4 Iris-versicolor FALSE
6.4 3.2 4.5 1.5 Iris-versicolor Iris-versicolor
6.9 3.1 4.9 1.5 Iris-versicolor FALSE
5.5 2.3 4 1.3 Iris-versicolor Iris-versicolor
6.5 2.8 4.6 1.5 Iris-versicolor Iris-versicolor
5.7 2.8 4.5 1.3 Iris-versicolor Iris-versicolor
6.3 3.3 4.7 1.6 Iris-versicolor Iris-versicolor
4.9 2.4 3.3 1 Iris-versicolor Iris-versicolor
6.6 2.9 4.6 1.3 Iris-versicolor Iris-versicolor
5.2 2.7 3.9 1.4 Iris-versicolor Iris-versicolor
5 2 3.5 1 Iris-versicolor Iris-versicolor
5.9 3 4.2 1.5 Iris-versicolor Iris-versicolor
6 2.2 4 1 Iris-versicolor Iris-versicolor
6.1 2.9 4.7 1.4 Iris-versicolor Iris-versicolor
5.6 2.9 3.6 1.3 Iris-versicolor Iris-versicolor
6.7 3.1 4.4 1.4 Iris-versicolor Iris-versicolor
5.6 3 4.5 1.5 Iris-versicolor Iris-versicolor
5.8 2.7 4.1 1 Iris-versicolor Iris-versicolor
6.2 2.2 4.5 1.5 Iris-versicolor Iris-versicolor
5.6 2.5 3.9 1.1 Iris-versicolor Iris-versicolor
5.9 3.2 4.8 1.8 Iris-versicolor Iris-versicolor
6.1 2.8 4 1.3 Iris-versicolor Iris-versicolor
6.3 2.5 4.9 1.5 Iris-versicolor FALSE
6.1 2.8 4.7 1.2 Iris-versicolor Iris-versicolor
6.4 2.9 4.3 1.3 Iris-versicolor Iris-versicolor
6.6 3 4.4 1.4 Iris-versicolor Iris-versicolor
6.8 2.8 4.8 1.4 Iris-versicolor FALSE
6.7 3 5 1.7 Iris-versicolor FALSE
6 2.9 4.5 1.5 Iris-versicolor Iris-versicolor
5.7 2.6 3.5 1 Iris-versicolor Iris-versicolor
5.5 2.4 3.8 1.1 Iris-versicolor Iris-versicolor
7 | P a g e
4.4 3 1.3 0.2 Iris-setosa Iris-setosa
5.1 3.4 1.5 0.2 Iris-setosa Iris-setosa
5 3.5 1.3 0.3 Iris-setosa Iris-setosa
4.5 2.3 1.3 0.3 Iris-setosa Iris-setosa
4.4 3.2 1.3 0.2 Iris-setosa Iris-setosa
5 3.5 1.6 0.6 Iris-setosa Iris-setosa
5.1 3.8 1.9 0.4 Iris-setosa Iris-setosa
4.8 3 1.4 0.3 Iris-setosa Iris-setosa
5.1 3.8 1.6 0.2 Iris-setosa Iris-setosa
4.6 3.2 1.4 0.2 Iris-setosa Iris-setosa
5.3 3.7 1.5 0.2 Iris-setosa Iris-setosa
5 3.3 1.4 0.2 Iris-setosa Iris-setosa
7 3.2 4.7 1.4 Iris-versicolor FALSE
6.4 3.2 4.5 1.5 Iris-versicolor Iris-versicolor
6.9 3.1 4.9 1.5 Iris-versicolor FALSE
5.5 2.3 4 1.3 Iris-versicolor Iris-versicolor
6.5 2.8 4.6 1.5 Iris-versicolor Iris-versicolor
5.7 2.8 4.5 1.3 Iris-versicolor Iris-versicolor
6.3 3.3 4.7 1.6 Iris-versicolor Iris-versicolor
4.9 2.4 3.3 1 Iris-versicolor Iris-versicolor
6.6 2.9 4.6 1.3 Iris-versicolor Iris-versicolor
5.2 2.7 3.9 1.4 Iris-versicolor Iris-versicolor
5 2 3.5 1 Iris-versicolor Iris-versicolor
5.9 3 4.2 1.5 Iris-versicolor Iris-versicolor
6 2.2 4 1 Iris-versicolor Iris-versicolor
6.1 2.9 4.7 1.4 Iris-versicolor Iris-versicolor
5.6 2.9 3.6 1.3 Iris-versicolor Iris-versicolor
6.7 3.1 4.4 1.4 Iris-versicolor Iris-versicolor
5.6 3 4.5 1.5 Iris-versicolor Iris-versicolor
5.8 2.7 4.1 1 Iris-versicolor Iris-versicolor
6.2 2.2 4.5 1.5 Iris-versicolor Iris-versicolor
5.6 2.5 3.9 1.1 Iris-versicolor Iris-versicolor
5.9 3.2 4.8 1.8 Iris-versicolor Iris-versicolor
6.1 2.8 4 1.3 Iris-versicolor Iris-versicolor
6.3 2.5 4.9 1.5 Iris-versicolor FALSE
6.1 2.8 4.7 1.2 Iris-versicolor Iris-versicolor
6.4 2.9 4.3 1.3 Iris-versicolor Iris-versicolor
6.6 3 4.4 1.4 Iris-versicolor Iris-versicolor
6.8 2.8 4.8 1.4 Iris-versicolor FALSE
6.7 3 5 1.7 Iris-versicolor FALSE
6 2.9 4.5 1.5 Iris-versicolor Iris-versicolor
5.7 2.6 3.5 1 Iris-versicolor Iris-versicolor
5.5 2.4 3.8 1.1 Iris-versicolor Iris-versicolor
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
8 | P a g e
5.5 2.4 3.7 1 Iris-versicolor Iris-versicolor
5.8 2.7 3.9 1.2 Iris-versicolor Iris-versicolor
6 2.7 5.1 1.6 Iris-versicolor FALSE
5.4 3 4.5 1.5 Iris-versicolor Iris-versicolor
6 3.4 4.5 1.6 Iris-versicolor Iris-versicolor
6.7 3.1 4.7 1.5 Iris-versicolor FALSE
6.3 2.3 4.4 1.3 Iris-versicolor Iris-versicolor
5.6 3 4.1 1.3 Iris-versicolor Iris-versicolor
5.5 2.5 4 1.3 Iris-versicolor Iris-versicolor
5.5 2.6 4.4 1.2 Iris-versicolor Iris-versicolor
6.1 3 4.6 1.4 Iris-versicolor Iris-versicolor
5.8 2.6 4 1.2 Iris-versicolor Iris-versicolor
5 2.3 3.3 1 Iris-versicolor Iris-versicolor
5.6 2.7 4.2 1.3 Iris-versicolor Iris-versicolor
5.7 3 4.2 1.2 Iris-versicolor Iris-versicolor
5.7 2.9 4.2 1.3 Iris-versicolor Iris-versicolor
6.2 2.9 4.3 1.3 Iris-versicolor Iris-versicolor
5.1 2.5 3 1.1 Iris-versicolor Iris-versicolor
5.7 2.8 4.1 1.3 Iris-versicolor Iris-versicolor
6.3 3.3 6 2.5 Iris-virginica Iris-virginica
5.8 2.7 5.1 1.9 Iris-virginica Iris-virginica
7.1 3 5.9 2.1 Iris-virginica Iris-virginica
6.3 2.9 5.6 1.8 Iris-virginica Iris-virginica
6.5 3 5.8 2.2 Iris-virginica Iris-virginica
7.6 3 6.6 2.1 Iris-virginica Iris-virginica
4.9 2.5 4.5 1.7 Iris-virginica FALSE
7.3 2.9 6.3 1.8 Iris-virginica Iris-virginica
6.7 2.5 5.8 1.8 Iris-virginica Iris-virginica
7.2 3.6 6.1 2.5 Iris-virginica Iris-virginica
6.5 3.2 5.1 2 Iris-virginica Iris-virginica
6.4 2.7 5.3 1.9 Iris-virginica Iris-virginica
6.8 3 5.5 2.1 Iris-virginica Iris-virginica
5.7 2.5 5 2 Iris-virginica Iris-virginica
5.8 2.8 5.1 2.4 Iris-virginica Iris-virginica
6.4 3.2 5.3 2.3 Iris-virginica Iris-virginica
6.5 3 5.5 1.8 Iris-virginica Iris-virginica
7.7 3.8 6.7 2.2 Iris-virginica Iris-virginica
7.7 2.6 6.9 2.3 Iris-virginica Iris-virginica
6 2.2 5 1.5 Iris-virginica Iris-virginica
6.9 3.2 5.7 2.3 Iris-virginica Iris-virginica
5.6 2.8 4.9 2 Iris-virginica Iris-virginica
7.7 2.8 6.7 2 Iris-virginica Iris-virginica
6.3 2.7 4.9 1.8 Iris-virginica Iris-virginica
8 | P a g e
5.5 2.4 3.7 1 Iris-versicolor Iris-versicolor
5.8 2.7 3.9 1.2 Iris-versicolor Iris-versicolor
6 2.7 5.1 1.6 Iris-versicolor FALSE
5.4 3 4.5 1.5 Iris-versicolor Iris-versicolor
6 3.4 4.5 1.6 Iris-versicolor Iris-versicolor
6.7 3.1 4.7 1.5 Iris-versicolor FALSE
6.3 2.3 4.4 1.3 Iris-versicolor Iris-versicolor
5.6 3 4.1 1.3 Iris-versicolor Iris-versicolor
5.5 2.5 4 1.3 Iris-versicolor Iris-versicolor
5.5 2.6 4.4 1.2 Iris-versicolor Iris-versicolor
6.1 3 4.6 1.4 Iris-versicolor Iris-versicolor
5.8 2.6 4 1.2 Iris-versicolor Iris-versicolor
5 2.3 3.3 1 Iris-versicolor Iris-versicolor
5.6 2.7 4.2 1.3 Iris-versicolor Iris-versicolor
5.7 3 4.2 1.2 Iris-versicolor Iris-versicolor
5.7 2.9 4.2 1.3 Iris-versicolor Iris-versicolor
6.2 2.9 4.3 1.3 Iris-versicolor Iris-versicolor
5.1 2.5 3 1.1 Iris-versicolor Iris-versicolor
5.7 2.8 4.1 1.3 Iris-versicolor Iris-versicolor
6.3 3.3 6 2.5 Iris-virginica Iris-virginica
5.8 2.7 5.1 1.9 Iris-virginica Iris-virginica
7.1 3 5.9 2.1 Iris-virginica Iris-virginica
6.3 2.9 5.6 1.8 Iris-virginica Iris-virginica
6.5 3 5.8 2.2 Iris-virginica Iris-virginica
7.6 3 6.6 2.1 Iris-virginica Iris-virginica
4.9 2.5 4.5 1.7 Iris-virginica FALSE
7.3 2.9 6.3 1.8 Iris-virginica Iris-virginica
6.7 2.5 5.8 1.8 Iris-virginica Iris-virginica
7.2 3.6 6.1 2.5 Iris-virginica Iris-virginica
6.5 3.2 5.1 2 Iris-virginica Iris-virginica
6.4 2.7 5.3 1.9 Iris-virginica Iris-virginica
6.8 3 5.5 2.1 Iris-virginica Iris-virginica
5.7 2.5 5 2 Iris-virginica Iris-virginica
5.8 2.8 5.1 2.4 Iris-virginica Iris-virginica
6.4 3.2 5.3 2.3 Iris-virginica Iris-virginica
6.5 3 5.5 1.8 Iris-virginica Iris-virginica
7.7 3.8 6.7 2.2 Iris-virginica Iris-virginica
7.7 2.6 6.9 2.3 Iris-virginica Iris-virginica
6 2.2 5 1.5 Iris-virginica Iris-virginica
6.9 3.2 5.7 2.3 Iris-virginica Iris-virginica
5.6 2.8 4.9 2 Iris-virginica Iris-virginica
7.7 2.8 6.7 2 Iris-virginica Iris-virginica
6.3 2.7 4.9 1.8 Iris-virginica Iris-virginica
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
9 | P a g e
6.7 3.3 5.7 2.1 Iris-virginica Iris-virginica
7.2 3.2 6 1.8 Iris-virginica Iris-virginica
6.2 2.8 4.8 1.8 Iris-virginica Iris-virginica
6.1 3 4.9 1.8 Iris-virginica Iris-virginica
6.4 2.8 5.6 2.1 Iris-virginica Iris-virginica
7.2 3 5.8 1.6 Iris-virginica Iris-virginica
7.4 2.8 6.1 1.9 Iris-virginica Iris-virginica
7.9 3.8 6.4 2 Iris-virginica Iris-virginica
6.4 2.8 5.6 2.2 Iris-virginica Iris-virginica
6.3 2.8 5.1 1.5 Iris-virginica Iris-virginica
6.1 2.6 5.6 1.4 Iris-virginica Iris-virginica
7.7 3 6.1 2.3 Iris-virginica Iris-virginica
6.3 3.4 5.6 2.4 Iris-virginica Iris-virginica
6.4 3.1 5.5 1.8 Iris-virginica Iris-virginica
6 3 4.8 1.8 Iris-virginica FALSE
6.9 3.1 5.4 2.1 Iris-virginica Iris-virginica
6.7 3.1 5.6 2.4 Iris-virginica Iris-virginica
6.9 3.1 5.1 2.3 Iris-virginica Iris-virginica
5.8 2.7 5.1 1.9 Iris-virginica Iris-virginica
6.8 3.2 5.9 2.3 Iris-virginica Iris-virginica
6.7 3.3 5.7 2.5 Iris-virginica Iris-virginica
6.7 3 5.2 2.3 Iris-virginica Iris-virginica
6.3 2.5 5 1.9 Iris-virginica Iris-virginica
6.5 3 5.2 2 Iris-virginica Iris-virginica
6.2 3.4 5.4 2.3 Iris-virginica Iris-virginica
5.9 3 5.1 1.8 Iris-virginica Iris-virginica
I found best results using RBF Network with Non-Normalized Gaussian activation function with 9
mismatches. And I found best results using MLP Network with 4 mismatches.
MLP Network as Second Layer
Random Center K Means Center
Non-Normalized Gaussian
function
9 9
Normalized Gaussian function 11 11
Support Vector Machine as Second Layer
Random Center K Means Center
Non-Normalized Gaussian
function
14 10
Normalized Gaussian function 14 17
9 | P a g e
6.7 3.3 5.7 2.1 Iris-virginica Iris-virginica
7.2 3.2 6 1.8 Iris-virginica Iris-virginica
6.2 2.8 4.8 1.8 Iris-virginica Iris-virginica
6.1 3 4.9 1.8 Iris-virginica Iris-virginica
6.4 2.8 5.6 2.1 Iris-virginica Iris-virginica
7.2 3 5.8 1.6 Iris-virginica Iris-virginica
7.4 2.8 6.1 1.9 Iris-virginica Iris-virginica
7.9 3.8 6.4 2 Iris-virginica Iris-virginica
6.4 2.8 5.6 2.2 Iris-virginica Iris-virginica
6.3 2.8 5.1 1.5 Iris-virginica Iris-virginica
6.1 2.6 5.6 1.4 Iris-virginica Iris-virginica
7.7 3 6.1 2.3 Iris-virginica Iris-virginica
6.3 3.4 5.6 2.4 Iris-virginica Iris-virginica
6.4 3.1 5.5 1.8 Iris-virginica Iris-virginica
6 3 4.8 1.8 Iris-virginica FALSE
6.9 3.1 5.4 2.1 Iris-virginica Iris-virginica
6.7 3.1 5.6 2.4 Iris-virginica Iris-virginica
6.9 3.1 5.1 2.3 Iris-virginica Iris-virginica
5.8 2.7 5.1 1.9 Iris-virginica Iris-virginica
6.8 3.2 5.9 2.3 Iris-virginica Iris-virginica
6.7 3.3 5.7 2.5 Iris-virginica Iris-virginica
6.7 3 5.2 2.3 Iris-virginica Iris-virginica
6.3 2.5 5 1.9 Iris-virginica Iris-virginica
6.5 3 5.2 2 Iris-virginica Iris-virginica
6.2 3.4 5.4 2.3 Iris-virginica Iris-virginica
5.9 3 5.1 1.8 Iris-virginica Iris-virginica
I found best results using RBF Network with Non-Normalized Gaussian activation function with 9
mismatches. And I found best results using MLP Network with 4 mismatches.
MLP Network as Second Layer
Random Center K Means Center
Non-Normalized Gaussian
function
9 9
Normalized Gaussian function 11 11
Support Vector Machine as Second Layer
Random Center K Means Center
Non-Normalized Gaussian
function
14 10
Normalized Gaussian function 14 17
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
10 | P a g e
Discussion
1. There are some drawbacks of unsupervised center selection in radial basis functions
2. We can use an SVM for the second layer instead of a perceptron but it is not efficient for more
than 2 classes classification
10 | P a g e
Discussion
1. There are some drawbacks of unsupervised center selection in radial basis functions
2. We can use an SVM for the second layer instead of a perceptron but it is not efficient for more
than 2 classes classification
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
11 | P a g e
Appendices
MATLAB Sourcecode for RBF Network with MLP Network
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
%Centers=C;
11 | P a g e
Appendices
MATLAB Sourcecode for RBF Network with MLP Network
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
%Centers=C;
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
12 | P a g e
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1) -Centers(2,1))^2 + (Centers(1,2) -Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4)-Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1) -Centers(3,1))^2 + (Centers(1,2) -Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4) -Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1)-Centers(2,1))^2 + (Centers(3,2) -Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4) -Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
d=zeros(1,3);
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98 -106) to use Non-Normalized Activation
%functions
%
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))));
end
end
12 | P a g e
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1) -Centers(2,1))^2 + (Centers(1,2) -Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4)-Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1) -Centers(3,1))^2 + (Centers(1,2) -Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4) -Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1)-Centers(2,1))^2 + (Centers(3,2) -Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4) -Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
d=zeros(1,3);
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98 -106) to use Non-Normalized Activation
%functions
%
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))));
end
end
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
13 | P a g e
% %
%Normalized method
%Summation
%Uncomment following lines (114 -130) to use Gaussian Normalized Activation
functions
% RBFNormSum=zeros(150,1);
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
% RBFNormSum(i,1)= exp( -(d(1,j)/(2*(sigma^2))))+ RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
%
% % calculate output for gaussian function
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
% RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))))/RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
RBFoutput
RBFo=RBFoutput.'
% making MLP network
% T=zeros(1,150);
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
S=[3 1]
;
R=[0 1;0 1;0 1]
% used feedforward neural network as MLP [3 1]
MLPnet=newff(RBFo,S);
MLPnet.trainParam.epochs = 500;
MLPnet.trainParam.lr = 0.1;
MLPnet.trainParam.mc = 0.9;
MLPnet.trainParam.show = 40;
13 | P a g e
% %
%Normalized method
%Summation
%Uncomment following lines (114 -130) to use Gaussian Normalized Activation
functions
% RBFNormSum=zeros(150,1);
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
% RBFNormSum(i,1)= exp( -(d(1,j)/(2*(sigma^2))))+ RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
%
% % calculate output for gaussian function
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
% RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))))/RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
RBFoutput
RBFo=RBFoutput.'
% making MLP network
% T=zeros(1,150);
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
S=[3 1]
;
R=[0 1;0 1;0 1]
% used feedforward neural network as MLP [3 1]
MLPnet=newff(RBFo,S);
MLPnet.trainParam.epochs = 500;
MLPnet.trainParam.lr = 0.1;
MLPnet.trainParam.mc = 0.9;
MLPnet.trainParam.show = 40;
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
14 | P a g e
MLPnet.trainParam.perf = 'mse';
MLPnet.trainParam.goal = 0.001;
MLPnet.trainParam.min_grad = 0.00001;
MLPnet.trainParam.max_fail=4;
MLPnet = train(MLPnet,RBFo,T);
%simulating neural network
y=sim(MLPnet,RBFo);
output=round(y.');
Target=T.';
compare= [T.' output]
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
MATLAB Source code for RBF Network with SVM
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function with Support Vector Machine
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
14 | P a g e
MLPnet.trainParam.perf = 'mse';
MLPnet.trainParam.goal = 0.001;
MLPnet.trainParam.min_grad = 0.00001;
MLPnet.trainParam.max_fail=4;
MLPnet = train(MLPnet,RBFo,T);
%simulating neural network
y=sim(MLPnet,RBFo);
output=round(y.');
Target=T.';
compare= [T.' output]
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
MATLAB Source code for RBF Network with SVM
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% Radial Basis Function with Support Vector Machine
[arr tx] = xlsread('data.xls');
Centers=zeros(3,4);
% I found centers as mean of the same cluster values
for i=1:50
Centers(1,1)=arr(i,1)+Centers(1,1);
Centers(1,2)=arr(i,2)+Centers(1,2);
Centers(1,3)=arr(i,3)+Centers(1,3);
Centers(1,4)=arr(i,4)+Centers(1,4);
end
for i=51:100
Centers(2,1)=arr(i,1)+Centers(2,1);
Centers(2,2)=arr(i,2)+Centers(2,2);
Centers(2,3)=arr(i,3)+Centers(2,3);
Centers(2,4)=arr(i,4)+Centers(2,4);
end
for i=101:150
Centers(3,1)=arr(i,1)+Centers(3,1);
Centers(3,2)=arr(i,2)+Centers(3,2);
Centers(3,3)=arr(i,3)+Centers(3,3);
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
15 | P a g e
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
Centers=C;
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1) -Centers(2,1))^2 + (Centers(1,2) -Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4) -Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1) -Centers(3,1))^2 + (Centers(1,2) -Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4) -Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1) -Centers(2,1))^2 + (Centers(3,2)-Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4) -Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
15 | P a g e
Centers(3,4)=arr(i,4)+Centers(3,4);
end
for j= 1:3
Centers(j,1)=Centers(j,1)/50;
Centers(j,2)=Centers(j,2)/50;
Centers(j,3)=Centers(j,3)/50;
Centers(j,4)=Centers(j,4)/50;
end
Centers
% OR we can use k means algorithms calculate cluster centers
k=3; %number of clusters
[IDX,C]=kmeans(arr,k);
C %RBF centres
%Uncomment following line to use k means
Centers=C;
% distance between hidden nodes
%distance between hidden node 1 & 2
dist1= sqrt((Centers(1,1) -Centers(2,1))^2 + (Centers(1,2) -Centers(2,2))^2 +
(Centers(1,3)-Centers(2,3))^2 + (Centers(1,4) -Centers(2,4))^2);
%distance between hidden node 1 & 3
dist2= sqrt((Centers(1,1) -Centers(3,1))^2 + (Centers(1,2) -Centers(3,2))^2 +
(Centers(1,3)-Centers(3,3))^2 + (Centers(1,4) -Centers(3,4))^2);
%distance between hidden node 3 & 2
dist3= sqrt((Centers(3,1) -Centers(2,1))^2 + (Centers(3,2)-Centers(2,2))^2 +
(Centers(3,3)-Centers(2,3))^2 + (Centers(3,4) -Centers(2,4))^2);
% finding maximum distance
maxdist=0;
if ( dist1>dist2) & (dist1>dist3)
maxdist=dist1;
end
if ( dist2>dist1) & (dist2>dist3)
maxdist=dist2;
end
if ( dist3>dist1) & (dist3>dist2)
maxdist=dist3;
end
% calculating width
sigma= maxdist/sqrt(2*3);
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
16 | P a g e
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98 -106) to use Non-Normalized Activation
%functions
d=zeros(1,3);
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))));
end
% d=[0 0 0];
end
%
%Normalized method
%Summation
%Uncomment following lines (114 -130) to use Gaussian Normalized Activation
functions
% RBFNormSum=zeros(150,1);
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
% RBFNormSum(i,1)= exp( -(d(1,j)/(2*(sigma^2))))+ RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
%
% % calculate output for gaussian function
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
% RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))))/RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
RBFoutput
RBFo=RBFoutput.'
% making SVM network
16 | P a g e
maxdist;
% Gaussian
%calculating outputs of RBF networks
RBFoutput=zeros(150,3);
d1=zeros(1,4);
Centers;
%Unnormalized method
% calculate output for gaussian function
%Uncomment following lines (98 -106) to use Non-Normalized Activation
%functions
d=zeros(1,3);
for i=1:150
for j=1:3
d(1,j)= (arr(i,1)- Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))));
end
% d=[0 0 0];
end
%
%Normalized method
%Summation
%Uncomment following lines (114 -130) to use Gaussian Normalized Activation
functions
% RBFNormSum=zeros(150,1);
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4) - Centers(j,4))^2;
% RBFNormSum(i,1)= exp( -(d(1,j)/(2*(sigma^2))))+ RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
%
% % calculate output for gaussian function
% for i=1:150
% for j=1:3
% d(1,j)= (arr(i,1) - Centers(j,1))^2 + (arr(i,2) - Centers(j,2))^2 +
(arr(i,3)- Centers(j,3))^2 + (arr(i,4)- Centers(j,4))^2;
%
% RBFoutput(i,j)= exp( -(d(1,j)/(2*(sigma^2))))/RBFNormSum(i,1);
% end
% % d=[0 0 0];
% end
RBFoutput
RBFo=RBFoutput.'
% making SVM network
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
17 | P a g e
group=cell(3,1)
group{1,1}=zeros(150,1);
for n=1:150;
tclass(n,1)=tx(n,5);
end
group{1,1}=ismember(tclass, 'Iris-setosa')
group{2,1}=ismember(tclass, 'Iris-versicolor')
group{3,1}=ismember(tclass, 'Iris-virginica')
[train, test] = crossvalind( 'holdOut',group{1,1});
cp = classperf(group {1,1});
for i=1:3
%svmStruct(i) =
svmtrain(RBFoutput(train,:),group{i,1}(train),'showplot',true);
svmStruct(i) = svmtrain(RBFoutput,group{i,1}, 'showplot',true);
end
for j=1:size(RBFoutput)
for k=1:3
if(svmclassify(svmStruct(k), RBFoutput(j,:)))
break;
end
end
result(j) = k;
end
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
compare=[T.' result.']
Target=T.'
output=result.'
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
MATLAB Source Code MLP Network
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% MLP Network
[arr tx] = xlsread('data.xls');
17 | P a g e
group=cell(3,1)
group{1,1}=zeros(150,1);
for n=1:150;
tclass(n,1)=tx(n,5);
end
group{1,1}=ismember(tclass, 'Iris-setosa')
group{2,1}=ismember(tclass, 'Iris-versicolor')
group{3,1}=ismember(tclass, 'Iris-virginica')
[train, test] = crossvalind( 'holdOut',group{1,1});
cp = classperf(group {1,1});
for i=1:3
%svmStruct(i) =
svmtrain(RBFoutput(train,:),group{i,1}(train),'showplot',true);
svmStruct(i) = svmtrain(RBFoutput,group{i,1}, 'showplot',true);
end
for j=1:size(RBFoutput)
for k=1:3
if(svmclassify(svmStruct(k), RBFoutput(j,:)))
break;
end
end
result(j) = k;
end
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
compare=[T.' result.']
Target=T.'
output=result.'
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
MATLAB Source Code MLP Network
clc
clear all
% M.K.H. Gunasekara
% AS2010377
% Machine Learning
% MLP Network
[arr tx] = xlsread('data.xls');
M.K.H.Gunasekara - AS2010377 CSC 367 2.0 Mathematical Computing
18 | P a g e
inputs=arr.';
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
%Multilayer network with hidden layer with 3 nodes
MLPnet=newff(inputs,[4 3 1]);
MLPnet.trainParam.epochs = 500;
MLPnet.trainParam.lr = 0.1;
MLPnet.trainParam.mc = 0.9;
MLPnet.trainParam.show = 40;
MLPnet.trainParam.perf = 'mse';
MLPnet.trainParam.goal = 0.001;
MLPnet.trainParam.min_grad = 0.00001;
MLPnet.trainParam.max_fail=4;
MLPnet = train(MLPnet,inputs,T);
%simulating neural network
y=sim(MLPnet,inputs);
output=round(y.');
Target=T.';
compare= [T.' output]
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
18 | P a g e
inputs=arr.';
T=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3]
%Multilayer network with hidden layer with 3 nodes
MLPnet=newff(inputs,[4 3 1]);
MLPnet.trainParam.epochs = 500;
MLPnet.trainParam.lr = 0.1;
MLPnet.trainParam.mc = 0.9;
MLPnet.trainParam.show = 40;
MLPnet.trainParam.perf = 'mse';
MLPnet.trainParam.goal = 0.001;
MLPnet.trainParam.min_grad = 0.00001;
MLPnet.trainParam.max_fail=4;
MLPnet = train(MLPnet,inputs,T);
%simulating neural network
y=sim(MLPnet,inputs);
output=round(y.');
Target=T.';
compare= [T.' output]
count=0;
for i=1:150
if(output(i)~=Target(i))
count=count+1;
end
end
Unmatched=count
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