Comments on the NIPALS algorithm
Article first published online: 30 MAR 2005
Copyright © 1990 John Wiley & Sons, Ltd.
Journal of Chemometrics
Volume 4, Issue 1, pages 97–100, January 1990
How to Cite
Miyashita, Y., Itozawa, T., Katsumi, H. and Sasaki, S.-I. (1990), Comments on the NIPALS algorithm. J. Chemometrics, 4: 97–100. doi: 10.1002/cem.1180040111
- Issue published online: 30 MAR 2005
- Article first published online: 30 MAR 2005
- Manuscript Revised: 7 AUG 1989
- Manuscript Received: 25 MAY 1989
- Matrix decomposition;
- Principal component;
The Non-linear Iterative Partial Least Squares (NIPALS) algorithm is used in principal component analysis to decompose a data matrix into score vectors and eigenvectors (loading vectors) plus a residual matrix. NIPALS starts with some guessed starting vector. The principal components obtained by NIPALS depends on the starting vector; the first principal component could not always be computed. Wold has suggested a starting vector for NIPALS, but we have found that even if this starting vector is used, the first principal component cannot be obtained in all cases. The reason why such a situation occurs is explained by the power method. A simple modification of the original NIPALS procedure to avoid getting smaller eigenvalues is presented.