First, I am aware that this can be done in sklearn - I'm intentionally trying to do it myself.
I am trying to extract the eigenvectors from
np.linalg.eig to form principal components. I am able to do it but I think there's a more elegant way. The part that is making it tricky is that, according to the documentation, the eigenvalues resulting from
np.linalg.eig are not necessarily ordered.
To find the first principal component (and second and so on) I am sorting the eigenvalues, then finding their original indexes, then using that to extract the right eigenvectors. I am intentionally reinventing the wheel a bit up to the point where I find the eigenvalues and eigenvectors, but not afterward. If there's any easier way to get from
e_vals, e_vecs = np.linalg.eig(cov_mat) to the principal components I'm interested.
import numpy as np np.random.seed(0) x = 10 * np.random.rand(100) y = 0.75 * x + 2 * np.random.randn(100) centered_x = x - np.mean(x) centered_y = y - np.mean(y) X = np.array(list(zip(centered_x, centered_y))).T def covariance_matrix(X): # I am aware of np.cov - intentionally reinventing n = X.shape return (X @ X.T) / (n-1) cov_mat = covariance_matrix(X) e_vals, e_vecs = np.linalg.eig(cov_mat) # The part below seems inelegant - looking for improvement sorted_vals = sorted(e_vals, reverse=True) index = [sorted_vals.index(v) for v in e_vals] i = np.argsort(index) sorted_vecs = e_vecs[:,i] pc1 = sorted_vecs[:, 0] pc2 = sorted_vecs[:, 1]