“Minimum Distance to Class Mean Classifier” is used to classify unclassified sample vectors where the vectors clustered in more than one classes are given. For example, in a dataset containing n sample vectors of dimension d some given sample vectors are already clustered into classes and some are not. We can classify the unclassified sample vectors with Class Mean Classifier.

1. Islamic University of Technology (IUT)
LAB#01
Designing a Minimum
Distance to Class Mean
Classifier
Mamunur Rashid (104420)
Date of Submission: 6/13/2014

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Table of Contents
Introduction ..................................................................................................................................................2
Task ...............................................................................................................................................................2
Solution.........................................................................................................................................................3
Step1 (Plotting two-class set of prototypes) ............................................................................................3
Step 2 (Calculating the distance from the calculated mean of each class using Linear Discriminant
Function)...................................................................................................................................................3
Step 3 (Drawing the decision boundary between the two-classes) .........................................................4
Matlab Code..................................................................................................................................................5
Conclusion:....................................................................................................................................................7

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Introduction
“Minimum Distance to Class Mean Classifier” is used to classify unclassified sample vectors
where the vectors clustered in more than one classes are given. For example, in a dataset
containing n sample vectors of dimension d some given sample vectors are already clustered
into classes and some are not. We can classify the unclassified sample vectors with Class Mean
Classifier.
Task
Given the following two-class set of prototypes
w1 = {(2, 2), (3, 1), (3, 3), (-1,-3), (4, 2), (-2, -2)}
w2 = {(0, 0), (-2, 2), (-1,-1), (-4, 2), (-4, 3), (2, 6)}
1. Plot all sample points from both classes, but samples from the same class should have the
same color and marker.
2. Using a minimum distance classifier with respect to ‘class mean’, classify the following points
by plotting them with the designated class-color but different marker.
X1 = (-1,-1)
X2 = (3, 2)
X3 = (-2, 1)
X4 = (8, 2)
Linear Discriminant Function:
3. Draw the decision boundary between the two-classes.

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Solution
Step1 (Plotting two-class set of prototypes)
Two classes were given. Firstly we plotted all the points. Samples from the same class were
plotted using the same color and marker so that different classes can be distinguished easily.
Here green solids represent class 1 and blue solids represent class 2.Figure of the corresponding
result:
Step 2 (Calculating the distance from the calculated mean of each class using Linear
Discriminant Function)
Now for each of the point (X1…X4) we calculated the distance from the calculated mean of each
class using Linear Discriminant Function.

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The point was assigned to a class with minimum distance from the respected class mean. For
better visualization, we used the same class color but different marker while plotting those
points. Here the triangular shapes are the given training samples. Class 1 and class 2 are green
and blue colored respectively.
Step 3 (Drawing the decision boundary between the two-classes)
Decision boundary between the two classes is to be drawn now. For finding out this boundary
we considered all possible points within the range considering those points as over the
boundary line whose distance from both the classes is same. However as the distance may not
be exactly the same, we used a threshold value to draw the approximate boundary between
the two classes. Here straight line created by red circles with blue dots represents the straight
line boundary between the two classes.

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Matlab Code
% Given two-class set of prototypes
w1 = [2 2; 3 1; 3 3; -1 -3; 4 2; -2 -2];
w2 = [0 0; -2 2; -1 -1; -4 2; -4 3; 2 6];
% Plot all sample points from both classes,
% samples from the same class should have the same color and marker
plot(w1(:,1),w1(:,2),'s','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g');
hold on;

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plot(w2(:,1),w2(:,2),'s','LineWidth',2,...
'MarkerEdgeColor','m',...
'MarkerFaceColor','b');
legend('class 1','class 2');
legend off;
% Calculating means of class 1 and 2
% and then assign them in y1 and y2 respectively
y1 = [ mean(w1(:,1)) mean(w1(:,2))];
y2 = [ mean(w2(:,1)) mean(w2(:,2))];
% Unclassified Samples
x = [-1 -1; 3 2; -2 1; 8 2];
% For n number of samples, calculate Linear Discriminant Function
for n = 1:4
g1 = x(n,:) * y1' - .5 * (y1 * y1');
g2 = x(n,:) * y2' - .5 * (y2 * y2');

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if g1 > g2
plot(x(n,1),x(n,2),'v','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g');
else
plot(x(n,1),x(n,2),'v','LineWidth',2,...
'MarkerEdgeColor','m',...
'MarkerFaceColor','b');
end
end
% Calculate decision boundary between two classes
d = [-4:2:8];
d = [d' 2 .* d' + 1.25];
plot(d(:,1),d(:,2),'--o','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','r');
legend('decision boundary');
hold off;
Conclusion:
This algorithm is very easy to implement and apply. As it conducts simple calculations, its’
calculation is apparently faster. The weakness of the algorithm is its misclassification rate is also
relatively higher because the boundary between the two classes is linear.