answer these quations with details

Assignment #3

1. Assuming the covariance matrix of a given class (w1) with three attributes as given below. Compute the principal components (Eigen vectors) and show that they are mutually orthogonal.

Cov =

1. Given the following data for two different classes (w1,w2)

X

Y =

Y =

X =

X =

1. Find distance between x1 = [5.5 3.2] from distribution 1 and its mean using Mahalanobis distance and the mean of class w1

2. Find distance between the mean values of the two distributions using Bhattacharya distance

3. Find the Fishers Linear Discriminant function

Bhattacharya Distance = between x1 and mu1 = (6.4 3.6)