corr2 return 1 for different value

why when i use corr2 for different value in matlab return result=1 although the tow matrix not similar like this:-

aa

aa =

  137.5093    1.9847

>> bb

bb =

  141.2252    3.3757

>> corr2(aa,bb)

ans =

     1

Answer 1

[Ameer Hamza]

If you use only 2D vectors with corr2(), it is always possible to draw a line connecting two points, so the correction coefficient is always 1 or -1. You can verify this by simplifying the formula: https://www.mathworks.com/help/releases/R2020a/images/ref/corr2.html#f1-227958 for the case when x and y are 2D vectors.

[Walter Roberson]

syms A [1 2]; syms B [1 2];
sum((A-mean(A)).*(B-mean(B)))
sqrt(sum((A-mean(A)).^2).*sum((B-mean(B)).^2))

This gives

2*(A1/2 - A2/2)*(B1/2 - B2/2)
2*((A1/2 - A2/2)^2*(B1/2 - B2/2)^2)^(1/2)

and by inspection you can see that these are the same value provided that the quantities are real-valued.

[khalida basheer]

Sir, thanks for the answer

Can you help me

I used the correlation coefficient for the purpose of matching in a system for identifying people

And I used the moments as features for the images

When I extract the person’s features and compare them by corr2 with the stored database, the result is completely identical to all people, or at least 99% identical, which is incorrect.

So in theory and without calculation, the features are different from one person to another

But I could not find a solution to this problem ???

[Walter Roberson]

The implication would be that either you have an error in extracting the features, or else that the features you are extracting are not useful for your purposes.

[khalida basheer]

Sir, when we look at the features they look similar to the pictures of the same person and at the same time different to everyone else

But when the correlation coefficient is found, the result is one, ( similarity of 100%).

For example in above example, aa it is the first two features of a person aa

And bb is the first two features of a person bb

In theory, they are different, but their correlation coefficient is 1

[Walter Roberson]

You need more than two features to use corr2()

[khalida basheer]

Sir, I used 7 features and you can see this example

These two feature vectors belong to two different people. You can see the result

Can you suggest me another method of matching that gives better results please?

K>> aa

aa = 2.4609 141.3396 3.7583 1.1016 0.3980 1.0616 0.1026

K>> bb

bb = 2.8913 165.9664 2.2820 2.2066 0.9156 0.4908 0.8817

K>> corr2(aa,bb)

ans =

0.9997

[Walter Roberson]

If you try something like

 [H,p] = ttest2(aa,bb)

you will get a p > 0.9 -- that is, if you treat the numbers as being a random distribution, there is more than a 90% chance that they come from the same random distribution.

The large value of the second feature dilutes the variation in the other features. If you take the correlation with the second feature removed, you will get a notably lower score. Perhaps you should rescale the second feature.

[khalida basheer]

Sir Walter Roberson, actually the problem is the second feature, after deleting it and relying on other features, I got the acceptable result

thank you very much