In python, How do we find the Correlation Coefficient between two matrices?

4
votes

I have got two matrices say, T1 and T2 each of size mxn. I want to find the correlation coefficient between two matrices
So far I haven't used any built-in library function for it. I am doing the following steps for it:
First I calculate the mean of the two matrices as: 

M1 = T1.mean()
M2 = T2.mean()

and then I subtract the mean from the corresponding matrices as: 

A = np.subtract(T1, M1)
B = np.subtract(T2, M2)

where np is the numpy library and A and B are the resulting matrices after doing the subtraction.
Now , I calculate the correlation coefficent as:

alpha = np.sum(A*B) / (np.sqrt((np.sum(A))*np.sum(B)))

However, the value i get is far greater than 1 and in not meaningful at all. It should be in between 0 and 1 to get some meaning out of it.
I have also tried to make use absolute values of matrix A and B, but that also did'nt work.
I also tried to use : 

np.sum(np.dot(A,B.T)) instead of np.sum(A*B)

in the numerator , but that also didn't work.
Edit1:
This is the formula that I intend to calculate:
This image shows the actual formula to be calculated

In this image, C is one of the matrices and T is another one.
'u' is the mean symbol.

Can somebody tell me where actually i am doing the mistake.

2
pythonnumpymatrixcorrelation
Do you want the correlation between the same row in each matrix? - gauteh
Or do you want just get the correlation between all values in A and all values in B? If so, just flatten both matrices into vectors and calculate the regular correlation coefficient - Simon
Please see the edit1 to give more insight into the problem - aamer aamer
Not 100% sure about this, but I think that np.sum(A*B) might actually do something else than what is shown in the formula. I guess that the first is calculating the sum of all elements after multiplying the two matrices, whereas the latter is summing up the multiplication of every single pair of values. Maybe you can check that with two very simple 2x2 matrices? - nostradamus

2 Answers

0
votes

Can you try this:

import numpy as np
x = np.array([[0.1, .32, .2, 0.4, 0.8], [.23, .18, .56, .61, .12]])
y = np.array([[2,4,0.1, .32, .2],[1,3,.23, .18, .56]])
pearson = np.corrcoef(x,y)
print(pearson)
0
votes

Well I think this function is doing what I intend for: 

def correlation_coefficient(T1, T2):
    numerator = np.mean((T1 - T1.mean()) * (T2 - T2.mean()))
    denominator = T1.std() * T2.std()
    if denominator == 0:
        return 0
    else:
        result = numerator / denominator
        return result

The calculation of numerator seems to be tricky here which doesn't exactly reflect the formula shown in the above image and denominator is just the product of standard deviations of the two images.
However, the result does make a sense now as the result lies only in between 0 and 1.