Activity 19 - Probabilistic Classification

In this activity, two set of classes are used and their pattern are recognized via the Linear Discriminant Analysis (LDA). The classification rule is used to "assign an object to the group with highest conditional probability"[1]. The formula used to classify an object to its group is given by:

where µ is the mean corrected value of an object, C is the pooled covariance matrix of all the groups and p is the classification probability. Two sets of sample were used; Vcut chips (Figure 1)
and Pillows (Figure 2). The criterion used to classify the objects are their Mean of the red and the green values.

Figure 1
Figure 2

The results of the classification is given by Table 1.
For the Training data, 100% classification was obtained as expected. But for the Test data, only 75% classification was obtained.
In conclusion, the LDA is a good method in classification of objects for random sample.

For this activity, I will give myself a grade of 8 because I did not obtain 100% classification for the test datas.

Appendix:
a = fscanfMat("F:\AP 186\act19\data1.txt");
b = fscanfMat("F:\AP 186\act19\data2.txt");
q = fscanfMat("F:\AP 186\act19\data4.txt");
c(1:4,1:2) = a(1:4,1:2);
c(5:8,1:2) = b(1:4,1:2);
mean_g = mean(c,'r');
a1(1:4,1:2) = a(1:4,1:2);
b1(1:4,1:2) = b(1:4,1:2);
mean_a1 = mean(a1,'r');
mean_b1 = mean(b1,'r');
for i = 1:2
mean_cora1(:,i) = a(:,i)-mean_g(i);
mean_corb1(:,i) = b(:,i)-mean_g(i);
end
c1 = (mean_cora1'*mean_cora1)/4;
c2 = (mean_corb1'*mean_corb1)/4;
for i = 1:2
for j = 1:2
C(i,j) = (4/8)*c1(i,j)+(4/8)*c2(i,j);
end
end

f(:,1) = ((((mean_a1)*inv(C))*c' )-(0.5*((mean_a1*inv(C))*mean_a1'))+log(0.5))';
f(:,2) = ((((mean_b1)*inv(C))*c' )-(0.5*((mean_b1*inv(C))*mean_b1'))+log(0.5))';