| Abstract |
Two-block PLS regression is a commonly used chemometrical method for multivariate calibration, structure activity relationships, data mining and other data analysis [2–6]. It models a response matrix, Y, as a linear combination of a set of X-variables, collected in the matrix X. Unlike multiple linear regression (MLR) which is based on the assumption of independence of the X-variables, PLS assumes just a linear relation between X and Y. Moreover, PLS assumes that X and Y are manifestations of the same set of underlying, latent variables (LVs), that is, the X and Y variables are related to each other via these LV’s. The LV model (one X block, single y-variable) assumed by PLS is shown below. X is the optionally scaled and centered matrix of predictor variables, for example, digitized spectra in a multivariate calibration application, and y is the vector of the single response variable, for example, the concentration being the target of the calibration, also optionally scaled and centered. E and f denote the residual matrix and vector of the X and y parts of the PLS model, respectively. |
| Referanse |
Wold, S., Høy, M., Martens, H., Trygg, J., Westad, F., MacGregor, J., Wise, B.M. 2009. The PLS model space revisited. Journal of Chemometrics, Vol 23, pp 67-68. |
Martin Høy
Harald Martens
