Discriminant Analysis

Question 1

When do you assign Xnew to group 1 (rather than group 2)?

Answer 1

λ(Xnew) = (mu1_ - mu2)^T * Σ^(-1) (Xnew - [mu1-mu2_]/2) > 0

Question 2

Where are misclassified elements represented in a confusion matrix?

Answer 2

Off-diagonal

Question 3

When do you allocate to group 1, group 2 and group 3?

Answer 3

Group 1 if h12(Xnew) >0, h13(Xnew) >0
Group 2 if h12(Xnew) <0, h23(Xnew) >0
Group 3 if h13(Xnew) <0, h23(Xnew) <0

Question 4

How can you improve a discriminant rule?

Answer 4

• relax assumptions

- use more variables if available

Question 5

Give the probability of misclassification?

Answer 5

1 - φ( (mu1_ - mu2_ )^T * Σ^(-1) * (mu1_ - mu2_ ) /2)