Principal components applied to modeling: Dealing with the mean vector

Principal components analysis is often used to fit a population of spectral reflectances by a mean vector plus a basis‐function expansion about the mean. Certain color‐technology applications (such as color correction) are much easier if the mean is absent. If the mean of reflectance (or of another spectral function) is a linear combination of the first few principal components (such as the first three), then a linear model can fit the original data without mentioning the mean vector in the model's formulation. This idea is worked out step by step, and a realistic example is presented.