How can we find the angle or orientation of the 1st Principal Component

How can I calculate the angle of the 1st Principal component found after PCA. I am using Princomp(). My data is a set of co-ordinates in 2D. For example, X={0,1,2,3,4,5,6,7,8,0}, Y=(0,2,3,2,2,3,2,2,2,0}.

Please advice how to calculate the angle/orientation of the 1st principal component. Thank you.

[Stephen]

There should be lot of books about the subject. This doesn't seem to be a matlab-related question.

Answer 1

[Aditya]

Hi Nabin,

To calculate the angle of the first principal component after performing PCA on a set of 2D coordinates, you can follow these steps. The angle gives you the orientation of the principal component in relation to the coordinate axes.

% Your data points
X = [0, 1, 2, 3, 4, 5, 6, 7, 8, 0];
Y = [0, 2, 3, 2, 2, 3, 2, 2, 2, 0];

% Combine into a matrix
data = [X' Y'];

% Perform PCA
[coeff, score, latent] = princomp(data);

% Extract the first principal component
firstPC = coeff(:, 1);

% Calculate the angle in radians
angleRad = atan2(firstPC(2), firstPC(1));

% Convert the angle to degrees
angleDeg = rad2deg(angleRad);

% Display the angle
disp(['Angle of the first principal component (in degrees): ', num2str(angleDeg)]);