Selecting significant factors by the noise addition method in principal component analysis

The noise addition method (NAM) is presented as a tool for determining the number of significant factors in a data set. The NAM is compared to residual standard deviation (RSD), the factor indicator function (IND), chi‐squared (χ2) and cross‐validation (CV) for establishing the number of significant factors in three data sets. The comparison and validation of the NAM are performed through Monte Carlo simulations with noise distributions of varying standard deviation, HPLC/UV‐vis chromatographs of a mixture of aromatic hydrocarbons, and FIA of methyl orange. The NAM succeeds in correctly identifying the proper number of significant factors 98% of the time with the simulated data, 99% in the HPLC data sets and 98% with the FIA data. RSD and χ2 fail to choose the proper number of factors in all three data sets. IND identifies the correct number of factors in the simulated data sets but fails with the HPLC and FIA data sets. Both CV methods fail in the HPLC and FIA data sets. CV also fails for the simulated data sets, while the modified CV correctly chooses the proper number of factors an average of 80% of the time. Copyright © 2001 John Wiley & Sons, Ltd.