Question

Given the following 3D input data, identify the principal component.

1 1 9

2 4 6

3 7 4

4 11 4

5 9 2

(Steps: center the data, calculate the sample covariance matrix, calculate the eigen vectors and eigen values, identify the principal component)

0.9138

-0.1035

0.3926

-0.2617

0.5891

0.7645

-0.4205

-0.6223

0.2342

-0.3105

-0.8014

0.5112

​

Answer 1

Answer:

center the data, calculate the sample covariance matrix, calculate the eigen vectors and eigen values, identify the principal component)

0.9138

-0.1035

0.3926

-0.2617

0.5891

0.7645

-0.4205

-0.6223

0.2342

-0.3105

-0.8014

0.5112

Explanation:

Answer 2

Answer:

-0.3105

-0.8014

0.5112

Explanation:

Center the data:

-2.0000 -5.4000 4.0000

-1.0000 -2.4000 1.0000

0 0.6000 -1.0000

1.0000 4.6000 -1.0000

2.0000 2.6000 -3.0000

Find the covariance matrix (((x − µ)

0

(x − µ))/(n − 1)):

2.5000 5.7500 -4.0000

5.7500 15.8000 -9.2500

-4.0000 -9.2500 7.0000

Solve characteristic equation to obtain the eigen values and eigen vectors

Eigen values:

0.1298

1.2415

23.9287

Eigen vectors:

0.9138 -0.2617 -0.3105

-0.1035 0.5891 -0.8014

0.3926 0.7645 0.5112

Select the principal component, i.e., the eigen vector corresponding to the largest eigen vlaue:

-0.3105

-0.8014

0.5112