https://doi.org/10.1351/goldbook.10156
Multivariate calibration in which a dependent variable is regressed against the scores of a chosen number of factors obtained from principal-component analysis of the predictor variable.
Notes:
- PCA decomposes the predictor variable data \(\boldsymbol{X}\) into \(k\) principal component factors \(\boldsymbol{\hat X}_{k} = \boldsymbol{T}_{k}\boldsymbol{P}_{k}^{\rm{T}}\), where \(k\) may be determined by cross validation. The dependent variable \(\boldsymbol{c}\) is then regressed against \(\boldsymbol{\hat X}_{k}\), \(\boldsymbol{c} = \boldsymbol{\hat X}_{k}\boldsymbol{\hat b}\).
- The factorization gives orthogonal factors, but no information about the predicted variable \(\boldsymbol{c}\) is used.
See also: multilinear regression, partial least squares