PCA measurement units

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Meritas
Posts: 6
Joined: Mon Oct 05, 2009 10:19 am

PCA measurement units

Postby Meritas » Mon Oct 05, 2009 10:36 am

Hi,

I am doing principal component analysis of variables that are all measured in the same units.

Just to make sure I am making the right inferences, could anyone please confirm or correct me?
If i use the covariance matrix for deriving PCA, I get principal component scores in original units, right? And if it is correlation matrix, then the principal component scores are unitless.

But still in each case we can interpret each of principal component score time series as a measure of deviation of the whole system of variables from the mean, is that correct?


Thank you in advance.

trubador
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Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm

Re: PCA measurement units

Postby trubador » Wed Oct 07, 2009 1:00 am

Meritas wrote:If i use the covariance matrix for deriving PCA, I get principal component scores in original units, right? And if it is correlation matrix, then the principal component scores are unitless.

Correct.

Meritas wrote:But still in each case we can interpret each of principal component score time series as a measure of deviation of the whole system of variables from the mean, is that correct?

I am not sure if we can intrepret the results in this way. What PCA does is to redistribute the total variance (sum of the variance of each variable) among the new components in descending order of importance. Therefore, when you use correlation matrix, the total variance will be equal to number of variables since each variable is standardized to zero mean and unit variance.


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