Question

2. Let 'x' now be a 2 dimensional feature, with class priors $p(\omega1) = 0.6$ and $p(\omega2) = 0.4$. Also $p(x|\omega1)$ and $p(x|\omega2)$ follow normal distributions with mean $(4, 11)$ and $(10, 3)$ respectively. [6] a. Let the covariance matrix $\Sigma1 = \Sigma2 = 3I$ ($I$ represents identity matrix). Given above information derive equations for (i) discriminant function and (ii) decision boundary for classification of a new 2D feature 'x'. b. If we change the class priors $p(\omega1)$ and $p(\omega2)$ how will it change (affect) the decision boundary? c. What is the effect of changing the covariance matrix $\Sigma1 != \Sigma2$ on the decision boundary? Note: support explanations for (b)& (c) with appropriate mathematical equations.

          2. Let 'x' now be a 2 dimensional feature, with class priors $p(\omega1) = 0.6$ and $p(\omega2) = 0.4$.
Also $p(x|\omega1)$ and $p(x|\omega2)$ follow normal distributions with mean $(4, 11)$ and $(10, 3)$ respectively. [6]
a. Let the covariance matrix $\Sigma1 = \Sigma2 = 3I$ ($I$ represents identity matrix). Given above information derive equations for (i) discriminant function and (ii) decision boundary for classification of a new 2D feature 'x'.
b. If we change the class priors $p(\omega1)$ and $p(\omega2)$ how will it change (affect) the decision boundary?
c. What is the effect of changing the covariance matrix $\Sigma1 != \Sigma2$ on the decision boundary?
Note: support explanations for (b)& (c) with appropriate mathematical equations.

2. Let 'x' now be a 2 dimensional feature, with class priors p(ω1) = 0.6 and p(ω2) = 0.4.
Also p(x|ω1) and p(x|ω2) follow normal distributions with mean (4, 11) and (10, 3) respectively. [6]
a. Let the covariance matrix Σ1 = Σ2 = 3I (I represents identity matrix). Given above information derive equations for (i) discriminant function and (ii) decision boundary for classification of a new 2D feature 'x'.
b. If we change the class priors p(ω1) and p(ω2) how will it change (affect) the decision boundary?
c. What is the effect of changing the covariance matrix Σ1 != Σ2 on the decision boundary?
Note: support explanations for (b) (c) with appropriate mathematical equations.

Added by Kimberly C.

Question

Please give Ace some feedback