How to index or retrive the original information after PCA

Hi all,

I have a question on using PCA. I have data set of 10,000X20. After using PCA, I compute the eigen values and it says 6 eigen values retains 85% of the information.

Now I need to know which 6 columns of the data are retained? I am just interested in obtaining the information about 6 columns of data (from the original data, which 6 columns have higher eigen values? For example are they 2, 3 5, 8, 15 and 20 etc) which have high eigen values. Is that possible using PCA?

Any help in this regard will be highly appreciated.

Kind regards

Ganesh

Answer 1

[the cyclist]

The way PCA works is not that you identify the N variables with the highest eigenvalues. Rather, you identify N linear combinations of your variables with the highest contribution. So, for principal component 1, it might be 48% of variable 1, plus 17% of variable 2, and so on. Then, for component 2, it might be 8% of variable 1 minus 35% of variable 2, and so on.

When you compute

coeff = pca(...)

each column tells you those coefficients for one component. In general, each component has at least a little bit of every original variable. You cannot say "only keep these 6".

Answer 2

[Ganesh]

Hi there, thanks for your answer. Are there any techniques which does the dimensional reduction based on the data where we can go back and index the actual information. I mean, after dimensional reduction can we able to see which column/row of the data has been reduced or redundant?

[the cyclist]

If you are trying to explain the variation of some other variable, then you may be able to use stepwise regression.

doc stepwisefit

for details on how to do this in MATLAB. (But you may want to read more generally about the technique, maybe on Wikipedia to start.)