I want to carry out PCA on a set of chemical data, some of them in oxide form and some in elemental form. The oxides are in percentage and the elements are in ppm.
I have understood that, the data have to be normalised/standardised before starting PCA. Now,
1) Should I have to convert all oxides to element first?
2) Should I have to convert all into single type of unit (either percentage or ppm )?
3) For normalisation, should I go for lognormal (10), lognormal (2) or natural log? What is the best way to decide which one is ideal?
4) If some elements show lognormal (10) distribution and some show Ln distribution, can I apply them separately or a single method to be followed for all?
5) Can I attempt IDF-Normal method for normalisation of such data?
Kindly advise.
For PCA, “normalization” is a technique to avoid adding up apples and pears.
PCA has no distributional assumption, but several other assumptions e.g. the underlying structure of the data must be linear.
Hello Ajoy,
A linear transformation of scores (e.g., from raw scores to z-scores) will not affect the relationship between scores from any pair of variables in your data set. Therefore, "standardization" is not necessary. PCA uses Pearson correlations as the measure of association, which represents a standardized covariance.
Normalization has several meanings, depending on context. If you're referring to the shape of score distributions, it is true that any pair of variables having different score distributions cannot have a perfect Pearson correlation. So, discrepant marginal distributions can attenuate the strength of observed correlations (and therefore impact how a resulting PCA or common factor analysis solution would turn out). If that's an issue, then you can decide how to deal with it. If not, carry on.
If you're referring to normalization in vectors, that has a completely different meaning (length of vector = 1), which would not apply.
Good luck with your work.
Dear David,
Thanx for your response.
Each variable in my dataset is positively skewed. Hence, I may have to bring it to a bell shape by some transformation, isn't it?
I assume, log transformation need to be tried, but which log?
Ln, Log10 or Log2?
And what if some of the variables show better fitting of curve in Log10 but some with Log2?
Regards,
Hello again Ajoy,
If it's important for scores to follow more closely a normal distribution, and transformation won't destroy some intrinsic meaning of the scale, then yes, try transforms. You won't see a marked among log transforms, since they differ only by a multiplicative constant (e.g, log(e) of 10 = 2.303, log(10) of 10 = 1.0, so the constant is 2.303). In some applications, base can be important, but in many it is arbitrary.
And yes, you can apply one transform to one variable and a different one to another, so long as your intention does not include comparing resultant values for level or spread.
Good luck with your work.
Hello Dr David,
Thanx again for clarifying my doubts. As I understood, it is better to consider raw data rather than transformed data when we are dealing with multiple variables at one go so that the natural variability is retained. Have I understood you correctly?
Secondly, some of my data are in oxide percentage (SiO2, FeO etc) and some are in elemental ppm (Cu, Mo, Cr etc), should I convert all of them into elemental ppm so that all the variables have the same unit?
Regards,
Dear Mr. Ajoy,
Technically, the decision to transform(standardization) or not, depends on what we see from the variance-covariance statistics of the variables. If you see a great difference in the variance between the variables. Then you should consider to standardized the data (simply transform the variance-covariance to correlation).
I have seen one example in a book by Johnson and wichern. Applying log to the data, with the original data takes value < o.ooo, that can cause the eigenvalues to have a value that far from 1. whereas, one of the criteria to retain the component is by looking at the eigenvalues > 1.
hope this may help.
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