Hotelling's T^2 scores in python

Question

I applied pca on a data set using matplotlib in python. However, matplotlib does not provide a t-squared scores like Matlab. Is there a way to compute Hotelling\'s T^2 score lik

Answer 1

Even though this is an old question, I am posting the code as it may help someone. Here is the code, as a bonus this does multiple hotelling tests at once

import numpy as np
from scipy.stats import f as f_distrib


def hotelling_t2(X, Y):

# X and Y are 3D arrays
# dim 0: number of features
# dim 1: number of subjects
# dim 2: number of mesh nodes or voxels (numer of tests)

nx = X.shape[1]
ny = Y.shape[1]
p = X.shape[0]
Xbar = X.mean(1)
Ybar = Y.mean(1)
Xbar = Xbar.reshape(Xbar.shape[0], 1, Xbar.shape[1])
Ybar = Ybar.reshape(Ybar.shape[0], 1, Ybar.shape[1])

X_Xbar = X - Xbar
Y_Ybar = Y - Ybar
Wx = np.einsum('ijk,ljk->ilk', X_Xbar, X_Xbar)
Wy = np.einsum('ijk,ljk->ilk', Y_Ybar, Y_Ybar)
W = (Wx + Wy) / float(nx + ny - 2)
Xbar_minus_Ybar = Xbar - Ybar
x = np.linalg.solve(W.transpose(2, 0, 1),
Xbar_minus_Ybar.transpose(2, 0, 1))
x = x.transpose(1, 2, 0)

t2 = np.sum(Xbar_minus_Ybar * x, 0)
t2 = t2 * float(nx * ny) / float(nx + ny)
stat = (t2 * float(nx + ny - 1 - p) / (float(nx + ny - 2) * p))

pval = 1 - np.squeeze(f_distrib.cdf(stat, p, nx + ny - 1 - p))
return pval, t2