Interpreting PLSR and PCR Solutions via Moore-Penrose Generalized Inverse
- Jong-Duk Kim
- Journal of The Korean Data Analysis Society (JKDAS)
- Vol.5 No.2
- 등재여부 : KCI등재
- 199 - 210 (12 pages)
This paper interprets partial least squares regression (PLSR) and principal component regression (PCR) solutions and data transformations in terms of Moore-Penrose generalized inverse. By finding a Moore-Penrose inverse of the matrix X ⁺ for the solution b = X ⁺ y in a rather backward way, matrix expressions for the transformed X matrices are provided and the way they alter the original X data is shown for the PLSR and PCR methods. A numerical example is given to illustrate how the transformation matrices and the transformed X matrices change as the number of components varies.
2. PLSR and PCR Solutions in terms of Generalized Inverse