PCA

Question 1

How do you find the eigenvalues of Matrix A?

Answer 1

Take the determinant of A, this will give a polynomial. Solve this polynomial to get the eigenvalues.

Question 2

How do you find the eigenvectors of Matrix A?

Answer 2

Any 2 element column vector in which the two elements have equal magnitude and opposite sign

Question 3

When doing PCA what format must the data be in?

Answer 3

A matrix where the columns are vectors and the rows are observations.

Question 4

Formula for Covariance

Answer 4

For every value in x, take every value in y, minus the mean of x from the current x value and multiply it by the current y value minus the mean of y. Divide the total by the number of data values - 1.

Question 5

Explain how to do PCA

Answer 5

Take the covaraince matrix of a dataset and find the eigenvalues. Normalise by divding each eigenvalue by the sum of the eigenvalues. Reduce the sets dimensionality by discarding low eigenvalues.