How does Hard Modeling Factor Analysis work?
This article answers a frequently asked question about the spectra analysis method Hard Modeling Factor Analysis (HMFA). It explains in a few steps what HMFA is and how it works. Spectral Hard Modeling methods – like HMFA and Indirect Hard Modeling (IHM) – are the reason why PEAXACT exists in the first place. There is a software tutorial available if you would like to try it on your own.
The Big Picture
HMFA can be used if you have a series of samples (e.g., from reaction monitoring) and you would like to calculate qualitative concentration profiles of the involved components. HMFA uses a Hard Model (a peak representation of a representative mixture sample) to analyze variations among all samples. As a result, it delivers estimates of the pure component spectra and concentration profiles.
HMFA is one of the less complex analysis methods because it requires nothing more than the data you would like to analyze.
Step 1: Building a Representative Hard Model
A representative spectral Hard Model is one that contains all peaks of all components occurring in the mixture spectrum, i.e., it represents all the spectral information of a mixture. The model is created by automatic peak fitting to a representative sample. (If such a sample does not exist, it can be computed from a series of mixtures.)
Representative sample (black, hardly visible), representative spectral Hard Model (red), individual model peaks in cyan are highlighted.
Step 2: Determining the Number of Components
If not known in advance, a Component Number Analysis helps to determine the number of components in a mixture. PEAXACT calculates the correlation among peaks and groups highly correlated peaks into components. Trying this for different component numbers reveals different errors and probabilities, which are helpful in finding the correct number of components.
Report plots of the Component Number Analysis.
Step 3: Calculating Pure Component Spectra and Concentration Profiles
After determining the total number of components, PEAXACT identifies pure component spectra from the associated peaks and calculates resulting concentration profiles for each component.
Calculated pure component spectra and concentration profiles.
Literature
- E. Kriesten, D. Mayer, F. Alsmeyer, C.B. Minnich, L. Greiner, and W. Marquardt (2008). “Identification of unknown pure component spectra by indirect hard modeling”, Chemometrics and Intelligent Laboratory Systems, Vol. 93, pp. 108–119.