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Short Communication
Comments on the NIPALS algorithm
Article first published online: 30 MAR 2005
DOI: 10.1002/cem.1180040111
Copyright © 1990 John Wiley & Sons, Ltd.
1099-128X/asset/cover.gif?v=1&s=2e3045c3733baa4258989f44bd61b29dd74ee736 "Journal of Chemometrics")
Additional Information
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
Publication History
- Issue published online: 30 MAR 2005
- Article first published online: 30 MAR 2005
- Manuscript Revised: 7 AUG 1989
- Manuscript Received: 25 MAY 1989
- Abstract
- References
- Cited By
Keywords:
- Matrix decomposition;
- NIPALS;
- Principal component;
- SIMCA;
- PLS
Abstract
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.