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

Abstract

SUMMARYThe 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), chisquared ( 2 ) 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 2 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.

Parallel Factor Analysis (PARAFAC) of Target Analytes in GC × GC−TOFMS Data: Automated Selection of a Model with an Appropriate Number of Factors

“…This results in “splitting” of an analyte signal across multiple factors and possible contamination of analyte signal with extraneous noise. To put this into context, the problem we address is the classical chemometrics problem of determining the most parsimonious model, i.e., the appropriate number of factors between underfitting and overfitting. ,,− It is important to remember, however, that PARAFAC models, unlike PCA-based models, are not nested, e.g., a one- or two-factor model cannot be extracted from a three-factor model. That is to say, a model with N factors can generally be said to have N unique components, none of which are exactly the same as any component in a N − x factor model (for N ≠ 1), where x is any positive integer from 1 to N − 1.…”