ASSume WT hawt Fhree classes, aneh Huo Adve nsionnk Baitinghoot Ah Follow ney means and Covacianet makaies :A mela, My = I! ; My = 15]p h I~)2-2 ne [0] ;poy Probabiliticy, J? (»)) = p (

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Answered Same DayOct 26, 2022

Answer To: ASSume WT hawt Fhree classes, aneh Huo Adve nsionnk Baitinghoot Ah Follow ney means and Covacianet...

Rhea answered on Oct 27 2022
62 Votes
Given, we have three classes, each 2d Gaussian having the following means and covariance matrices-
 and
Prior probabilities:
Let,
We need to-
1. Find linear discriminant functions and then graph the decision boundary regions.
The linear discriminant function for each class is-
Since, , so the covariance is class-independent and hence we can drop the terms which do not contain mean or prior probabilities as irrelevant.
Similarly, we can find and . Solving for separately for and we’ll get the decision boundary.
Using Matlab, we obtain the following-
mu1=[1;3];
mu2=[-1;6];
mu3=[-2;5];
sigma1=[1,-1;-1,4];
sigma2=[1,-1;-1,4];
sigma3=[1,-1;-1,4];
p1=1/5;
p2=1/5;
p3=3/5;
syms x1 x2;
g1 = -0.5*([x1;x2]-mu1)'*[inv(sigma1)*([x1;x2]-mu1)]-log(2*pi)-0.5*log(det(sigma1))+log(p1)
g2 =...
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