NaN result on xcorr?

Hello everyone. I am trying to use both xcorr(var1,var2,0,'coeff' and corrcoef in order to get a correlation coefficient of two vectors (I want to see how "similar" they are).

The thing is, sometimes I need to insert a vector of zeros into that calculation and the I get NaN as a result.

It is very important for me to be able to correlate between a vector of zeros and a vector of really small numbers ( both of same length, of course), and get a relatively good correlation between the two (relative to a vector of ones with a vector of small numbers, for example).

Answer 1

[Wayne King]

If you have a a vector of zeros, then using the 'coeff' option will give you NaNs because you are normalizing by the product of the input norms. The norm of the zero vector is 0 (it is the only vector with zero norm by the definition of a norm).

So you have a vector of 0/0

You can use the 'unbiased', 'biased', or 'none' options (the last one does not need to be specified), but you will get a vector of zeros of course.

If you cross correlate any vector with the zero vector, the answer must be a vector of zeros. How can it be anything else? The cross correlation involves an element-by-element product and sum. All your products must be zero if one of the inputs is the zero vector.

[Guy]

Hey Wayne,

Thank you for your answer, I understand that maybe the procedure of the correlation function is not suitable in my case.

Here is a brief of what I am dealing with:

I am receiving (to a function) a sequence of pairs of vectors that represent points of lines, and so I need to correlate each one of them with a previously known line vector and take the best fit every time.

The problem is that sometimes one of the pairs is a vector of zeros, and, alas, in some occasions it is the best fit. What can I do? I must detect it somehow..

Any ideas? What would be the best alternative?

[Wayne King]

If these are just points on a line, what not just orthogonally project each line onto the reference line?; that will give you the best approximation in the minimum squared error (2-norm) sense

[Guy]

Can you detail a little further? How do I do that?

Also forgot to mention, I figured the problem with the correlation might be a devision by zero, so I transferred zero vectors into 'eps' vectors, meaning that I gave them some insignificant value that will not have any affect on the desirable result. The outcome then was -1, which I could not understand because I correlated it with a vector of small values as well. Anyway, this did not work for me but maybe your idea will?