Compute correlations of several vectors-CodePudding

I have several pairs of vectors (arranged as two matrices) and I want to compute the vector of their pairwise correlation coefficients (or, better yet, angles between them - but since correlation coefficient is its cosine, I am using numpy.corrcoef):

np.array([np.corrcoef(m1[:,i],m2[:,i])[0,1]
          for i in range(m1.shape[1])])

I wonder if there is a way to "vectorize" this, i.e., avoid calling corrcoef several times.

CodePudding user response：

Instead of using np.corrcoef, you can write your own function that does the same thing. The calculation for the correlation coefficient of two vectors is quite simple:

linear correlation coefficient

Applying that here:

def vec_corrcoef(X, Y, axis=1):
    Xm = np.mean(X, axis=axis, keepdims=True)
    Ym = np.mean(Y, axis=axis, keepdims=True)
    N = np.sum((X - Xm) * (Y - Ym), axis=axis)
    D = np.sqrt(np.sum((X - Xm)**2, axis=axis) * np.sum((Y - Ym)**2, axis=axis))
    return N / D

To test:

m1 = np.random.random((100, 10))
m2 = np.random.random(m1.shape)

a = vec_corrcoef(m1, m2)
b = [np.corrcoef(v1, v2)[0, 1] for v1, v2 in zip(m1, m2)]

print(np.allclose(a, b)) # True