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Re: Covariance Matrix [message #86849 is a reply to message #86847]

Sat, 07 December 2013 06:37

amin farhang
Messages: 39
Registered: November 2010

Member

Hi David,

Indeed there is no any B vector in my problem. In statistical notes, for computing the covariance of a vector the following formula can be used:
cov(A,A) = E[(A-EA)*(A-EA)^T]
where E means expected value, EA is the mean value of A vector and T means transpose of A vector. I write a code for this (A is a column vector):

s = size(A)
Na = s[2]
MeanValue = total(A)/float(Na)
AT = transpose(A)
A = A - MeanValue
AT = AT - MeanValue
covariance = A ## AT

for example for A=[1,2,3,4] the covariance matrix with above code become:

2.25000 0.750000 -0.750000 -2.25000
0.750000 0.250000 -0.250000 -0.750000
-0.750000 -0.250000 0.250000 0.750000
-2.25000 -0.750000 0.750000 2.25000

but the weird thing is that if we divide the covariance matrix by standard deviation of A and AT we should see the correlation matrix.
in above example std(A) = 1.29 so correlation(A) = COV(A)/(std * std):

1.74419 0.581395 -0.581395 -1.74419
0.581395 0.193798 -0.193798 -0.581395
-0.581395 -0.193798 0.193798 0.581395
-1.74419 -0.581395 0.581395 1.74419

but we know that the correlation coefficients must be between -1 and 1 (diagonal elements must be equal to 1) but you see that in addition to being 1 in diagonal, the off-diagonal are greater than 1 in some cases!!

what is happening? how can I compute correct covariance that with conversion to correlation matrix all elements be in correct range?

or is it a code in IDL for computing the correlation matrix of vector?

Thanks,

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[Message index]

		Covariance Matrix By: amin farhang on Sat, 07 December 2013 04:11
		Re: Covariance Matrix By: David Fanning on Sat, 07 December 2013 05:31
		Re: Covariance Matrix By: amin farhang on Sat, 07 December 2013 06:37
		Re: Covariance Matrix By: Matthew Argall on Sat, 07 December 2013 07:28
		Re: Covariance Matrix By: amin farhang on Sat, 07 December 2013 09:25
		Re: Covariance Matrix By: Matthew Argall on Sat, 07 December 2013 09:38
		Re: Covariance Matrix By: Matthew Argall on Sat, 07 December 2013 09:46
		Re: Covariance Matrix By: amin farhang on Sun, 08 December 2013 11:57
		Re: Covariance Matrix By: haval.js on Tue, 04 March 2014 05:44
		Re: Covariance Matrix By: Matthew Argall on Tue, 04 March 2014 06:22
		Re: Covariance Matrix By: haval.js on Wed, 05 March 2014 02:37
		Re: Covariance Matrix By: haval.js on Wed, 05 March 2014 02:38
		Re: Covariance Matrix By: haval.js on Wed, 05 March 2014 02:43
		Re: Covariance Matrix By: Matthew Argall on Wed, 05 March 2014 05:14
		Re: Covariance Matrix By: haval.js on Mon, 10 March 2014 03:11
		Re: Covariance Matrix By: haval.js on Wed, 05 March 2014 02:39
		Re: Covariance Matrix By: andrei.makeev on Mon, 28 September 2015 11:26

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