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| Monday, October 13, 2008 |
| Activity 19: Linear Discriminant Analysis |
Moving on to our discussion about pattern recognition we study Linear Discriminant Analysis or LDA. Here we create a discriminant function from predictor variables. Here I tried classifying 5 centavo and 25 centavo coins.
This time since both are (should be) circular, I remove the parameter of Height over Width leaving three parameters for classifications: Area, R (NCC) and G (NCC). The code I used is shown below:
x = [1239 0.602028 0.283912;
1224 0.629195 0.280192;
1206 0.611142 0.289349;
2080 0.520683 0.374020;
2064 0.529127 0.382716;
1977 0.582884 0.345742];
xt = [1264 0.633988 0.271862;
1179 0.618832 0.278147;
1191 0.615691 0.280110;
2000 0.499452 0.372944;
1956 0.499452 0.379350;
1906 0.522208 0.392979];//Test class
y = [1;
1;
1;
2;
2;
2;];
x1 = [1239 0.602028 0.283912;
1224 0.629195 0.280192;
1206 0.611142 0.289349];
x2 = [2080 0.520683 0.374020;
2064 0.529127 0.382716;
1977 0.582884 0.345742];
n1 = size(x1, 1);
n2 = size(x2, 1);
m1 = mean(x1, 'r');
m2 = mean(x2, 'r');
m = mean(x, 'r');
x1o = x1 - mtlb_repmat(m, [n1, 1]);
x2o = x2 - mtlb_repmat(m, [n2, 1]);
c1 = (x1o'*x1o)/n1;
c2 = (x2o'*x2o)/n2;
C = (n1/(n1+n2))*c1 + (n2/(n1+n2))*c2;
p = [n1/(n1+n2); n2/(n1+n2)];
CI = inv(C);
for i = 1:size(xt, 1)
xk = xt(i, :);
f1(i) = m1*CI*xk' - 0.5*m1*CI*m1' + log(p(1));
f2(i) = m2*CI*xk' - 0.5*m2*CI*m2' + log(p(2));
end
class = f1 - f2;
class(class >= 0) = 1;
class(class < 0) = 2;
Again, 100% classification was shown.
Acknowledgments
Thanks to Ed for the code! I totally rocked this activity! I give myself 10/10 neutrinos!
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posted by poy @ 12:41 AM  |
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