Implementation of Minimum Distance classifier to Class Mean Classifier using python

1. Designing a Minimum Distance to Class Mean
Classifier
Dipesh Shome
Department of Computer Science and Engineering
Ahsanullah Univarsity of Science and Technology
Dhaka, Bangladesh
160204045@aust.edu
Abstract—Minimum distance to mean classifier is classifica-
tion process in which the mean point is calculated for known
classes.Then unknown classes are assigned to the class which
is arithmetically closest to the mean value of a class. In this
experiment, we use linear discriminant function to classify test
data.Then plot decision boundary and found accuracy of 85/
Index Terms—minimum distance classifier,linear discriminant
function,decision boundary
I. INTRODUCTION
In minimum distance classifier to mean class, training is
done using the feature vector of known class.Each class is
denoted by its mean vector.Then mean of the feature vectors
for the object within the class is calculated. When unknown
sample come, the sample is classified by measuring the closest
mean vector.It is a simple classification and used to classify
unclassified sample when distribution of the classes form
spherical shape.
II. EXPERIMENTAL DESIGN / METHODOLOGY
A. Description of the different tasks:
Two-class set of prototypes have to be taken from “train.txt”
and “test.txt” files.
Task 1: Plot all sample points (train data) from both
classes, but samples from the same class should have the
same color and marker.
Task 2: Using a minimum distance classifier with respect to
‘class mean’, classify the test data points by plotting them
with the designated class-color but a different marker. Use
the Linear Discriminant Function given below. Also, plot the
class means.
gi(X) = X|
Ȳi −
1
2
Ȳi
|
Ȳi
Task 3:Draw the decision boundary between the two classes.
Task 4:Find accuracy.
B. Implementation
1) Plotting of all sample data of train data: Here we have
a training dataset which is consist of 12 samples belong to two
different classes. First task is to plot all the data point of both
class.For plotting we import two python library: Numpy and
Matplotlib. Scatter plot function and marker were used to plot
the samples from same classes with same color. Train class 1
is plotted using dot(.) marker with red color and train class
2 is plotted using star(*) marker with blue color.Finally, we
legend the plot and the plotted figure is given in Fig.1.
Fig. 1. Sample point Plotting
2) Test data classification and calculating the distance from
mean of each class using Linear discriminant function: In task
2, First we calculate the mean of each class and plot with same
class color.The mean point of class 1 is represented by marker
’1’ with red color and Class 2 mean point is represented in ’D’
with blue color. Then calculate the distance from the mean of
each class for each test sample using the Linear discriminant
function.
gi(X) = X|
Ȳi −
1
2
Ȳi
|
Ȳi
I modified the discriminant function for my task and for
two class the discriminant function became,
g1(X) = ¯
w1
|
x −
1
2
¯
w1
|
¯
w1
g2(X) = ¯
w2
|
x −
1
2
¯
w2
|
¯
w2
Decision Rule for classify test data is as,if g1(X) > g2(X)
then, X belongs to class 1

2. else
X belongs to class 2
Fig. 2. Decision Boundary plotting
3) Decision boundary drawing between two classes: For
decision boundary drawing, i consider all the possible point
within the range as those points maintain equal distance from
both classes.Then i used the maximum and minimum value
of x to calculate y using the following function for drawing
boundary line between two class
g1(x) = g2(x)
= ¯
w1
|
x −
1
2
¯
w1
|
¯
w1 − ¯
w2
|
x +
1
2
¯
w2
|
¯
w2
= ( ¯
w1
|
− ¯
w2)x −
1
2
( ¯
w1
|
¯
w1 − ¯
w2
|
¯
w2)
Now we can consider it as linear equation to determine the
decision boundary:
( ¯
w1
|
− ¯
w2)x −
1
2
( ¯
w1
|
¯
w1 − ¯
w2
|
¯
w2) = 0
Where ( ¯
w1
|
− ¯
w2) is coefficients and 1
2 ( ¯
w1
|
¯
w1 − ¯
w2
|
¯
w2)
is constant.The final equation is look like
y =
coefficient1 ∗ x + constant
coefficient2
After plotting the x and y values, a straight line equation
is created with red dot which represent the decision boundary
between two class.
III. RESULT ANALYSIS
Test data is consist of seven sample points and two
classes.six out seven data point is correctly classified using
minimum distance classifier and all the training sample is
classified correctly.So, we can say that accuracy is 85/
Fig. 3. Plotting of mean of the classes and test data using minimum distance
classifier with respect to class mean
IV. CONCLUSION
In this experiment, i tried to implement a simple minimum
distance to class mean classifier without complex mathe-
matical calculation.Here, some sample classified accurately
and some classified wrongly but the calculation speed is
too faster.The limitation of this classifier is its accuracy rate
is comparatively lower in nonlinear dataset as the decision
boundary between two class is linear
V. ALGORITHM IMPLEMENTATION / CODE

3. REFERENCES
[1] Vladimir Curic,“Classification Slide,”
[2] Minimum Distance Classifier, ”http://sar.kangwon.ac.kr/etc/rsnote/rsnote/cp11/cp11−
6.htm : : text = The