after apply pca on a matrix,does any way exist to understand each column refers to which column in initial matrix? ?

hi i have an initial matrix A (63*9),i want to reduce it to 63*5,so i have used PCA:

[COEFF SCORE LATENT] = princomp(A);

pc=COEFF(:,1:5);

reduced-A=A*pc;

i use 'reduced-A' az my new matrix,is it true? and is there any way to find out each column in 'reduced-A' refer to which column in 'A'? for example the first column in 'reduced-A' come from which column in 'A'?

please help me

[Azzi Abdelmalek]

You can't use reduced-A as a matrix maybe you mean reduced_A?

Answer 1

[nick]

Hi sorena,

I understand that you want to know about the relationship between columns in 'reduced_A' and columns in A. When you apply PCA to a matrix, each column in the reduced matrix is linear combination of orginal columns. You can look at the 'pc' matrix , which contains the eigenvectors of covariance of matrix 'A'.

The elements in each column of 'pc' are weights that describe how much each original variable contributes to the principal componennt. For example, the first column of 'reduced_A' is a combination of all columns in 'A' weighted by the first column of 'pc'.

You can refer to the following documentation to know about the relationship between columns in 'PCA' :

https://medium.com/analytics-vidhya/understanding-principle-component-analysis-pca-step-by-step-e7a4bb4031d9