Loop Principal Component Analysis

Hello,

I would like to do a principal component analysis. The matrix is of 50x50 dimension. I don't want Matlab to run the PCA on the whole 50x50 Matrix but perform it from rows 1-10 then from 11-20 and so forth up until row 50. I tried around using loops. However, I did not arrive at my desired result which is a matrix that consists of 5 rows and 50 colums. They first row would contain the coefficients of the first component retrieved from the 1-10 pca, the second row would contain the first components for the 11-20 pca and so on…. Any chance somebody could give me a hint? Thank you very much Stefan

Answer 1

[Kevin Holst]

I'd suggest looking at the help page a little more for PCA:

http://www.mathworks.com/help/toolbox/stats/princomp.html

"COEFF = princomp(X) performs principal components analysis (PCA) on the n-by-p data matrix X, and returns the principal component coefficients, also known as loadings. Rows of X correspond to observations, columns to variables. COEFF is a p-by-p matrix, each column containing coefficients for one principal component. The columns are in order of decreasing component variance."

EDIT

by first component of the 1-10 analysis, do you mean the first row of the coefficients? If so, I think this will work for you:

for i = 1:size(x,1)/10  % this assumes the number of rows is ALWAYS a multiple of 10
[COEFFnew,SCOREnew,latentnew] = princomp(x((i-1)*10+1,i*10));    % if you don't need SCOREnew or latentnew, you can just leave those off
coeff(i,:) = COEFFnew(1,:);
end

coeff should be a 5x50 for your example of a 50x50 matrix, but the same code will also expand to a 1000x1000

[stefan strasser]

Thank you Kevin,

already checked on that one….if i just run the princomp command it performs pca on the whole matrix!however, i need princomp for rows 1-10,11-20,21-30,31-40 and 41-50. out of these individual results i need a matrix that consists of row 1= 1st component of the 1-10 analysis/2nd row 1st component of the 11-20 pca and so on and so on…finally it would be a 5x50 matrix consisting of the COEFFs as you mentioned correctly.... i need to work something out using a loop since my final data set will contain thousands of rows/assets and there is no way i could do that manually…

best regards,

stefan

[stefan strasser]

%pca looped

this is what i had in mind as a loop…BUT: how to proceed so that i receive the desired matrix?

for t=11:10:50

[COEFFnew,SCOREnew,latentnew] = princomp(x(((t-10):(t-1)),:))

end

Answer 2

[George McFadden]

The easiest way would be to divide your matrix in to 5 matrices, each 10x50. Then do a for loop that calls each matrix.

    Example:
      %variable =50x50
      v{1}=variable(1:10,:);v{2}=variable(11:20,:); %etc.

      %then perform loop
      for i=1:length(v)
      [coeff,score,latent,explained]=pca(v{i});
      end

[George McFadden]

Oops! You would have to assign the pca results to a new variable for each iteration. So...

Example: %variable =50x50 v{1}=variable(1:10,:);v{2}=variable(11:20,:); %etc. %then perform loop for i=1:length(v) [coeff{i},score{i},latent{i},explained{i}]=pca(v{i}); end