Non-linear iterative partial least squares

In statistics, non-linear iterative partial least squares (NIPALS) is an algorithm for computing the first few components in a principal component or partial least squares analysis. For very-high-dimensional datasets, such as those generated in the 'omics sciences (e.g., genomics, metabolomics) it is usually only necessary to compute the first few principal components. The nonlinear iterative partial least squares (NIPALS) algorithm calculates t₁ and p₁' from X. The outer product, t₁p₁' can then be subtracted from X leaving the residual matrix E₁. This can be then used to calculate subsequent principal components.^{[1] [2]} This results in a dramatic reduction in computational time since calculation of the covariance matrix is avoided.

References

1. ↑ Geladi, Paul; Kowalski, Bruce (1986), "Partial Least Squares Regression:A Tutorial", Analytica Chimica Acta 185: 1–17, doi:10.1016/0003-2670(86)80028-9 
2. ↑ Wold, Svante; Esbensen, Kim (1987), "Principal Component Analysis", Chemometrics and Intelligent Laboratory Systems 2: 37–52, doi:10.1016/0169-7439(87)80084-9 

External links

• Teach Me Data Analysis - The NIPALS Algorithm
• NIPALS algorithm for PLS regression
• Principal Component Analysis (PCA) and NIPALS algorithm
• Comments on the NIPALS algorithm (requires subscription)