Evolving Factor Analysis, Classical EFA

The basic principle of EFA is very simple. Instead of subjecting the complete matrix Y to the Singular Value Decomposition, specific sub-matrices of Y are analysed. In the original EFA, these sub-matrices are formed by the first i spectra of Y where i increases from 1 to the total number of spectra, ns. The appearance of a new compound during the acquisition of the data is indicated by the emergence of a new significant singular value. 

The example used for the introduction of EFA is based on the three-component chromatogram, Data Chrom2. m (p.219) we have used several times earlier. 

While most of the Matlab listing in Main EFAl, m is close to self explanatory, a few statements might need clarification. The singular values are stored in the matrix EFA f which has ns rows and ne columns. It is advantageous to plot the logarithms of the singular values their values span several orders of magnitude and cannot be represented in a normal plot. 

The rank is the number of significant singular values. The significance level can be estimated as the first non-significant singular value of the total matrix Y. 

The human eye is very good at detecting patterns - in this case the appearance of a new significant singular value. The appearance of a new component, as indicated by the point where a new significant singular value rises above the noise level, is delayed by increasing noise. 

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