Hi all, I would like to study the PCA to find out the VaR. But some terms in PCA such as factor scores, factor loadings, principal component loadings and principal component factors confuse me. Can any one state the definition of them ? Or Suggest some reference to me.For example, we use the svd method to decompose D such that D = UEV’, where D is 500 x 15 matrix (500 datas and 15 variables), U is 500 x 15 matrix, E is 15 x 15 diagonal matrix and V is 15 x 15 matrix. Please state the name of D, U and E in PCA. (which matrix is principal component factors, factor score, or factor loadings etc...)Many Thanks!!

I learnt PCA with the textbook by Johnson, D.E. (1998) "Applied Multivariate Methods for Data Analysis". It devots a chapter to this topic, however without a finance focus. Another textbook is Alexander, C. (ISBN 0-471-89975-5) that devotes a chapter example to finance.

PCAdunno if that's good, but it's a start (thanks, google). the nth principal component is just the eigenvector corresponding to the nth largest eigenvalue of a matrix. interesting generalizations include kernel PCs, principal curves, and in infinite dimensions, the karhunen-loeve decomposition.