In order to estimate the concentrations in the first four samples it is important to know that the scores are only uniquely determined up to a scaling and permutation indeterminacy.
If we do not know the concentration in any sample there is no way of fixing the level. However, in this case we assume that we know that the concentration of tryptophan in the fifth sample is
Assume that the first column in the score matrix
A, refers to tryptophan. Then by scaling this score vector such that the fifth element equals
y(5,1) then the remaining scores are estimates of the concentrations.
Thus by scaling such that
TrpConcEst = A(:,1)/A(5,1)*y(5,1);
the appropriate scaling is achieved. In reality, we do not know if it is the first component that corresponds to tryptophan so we have to figure out which component is tryptophan by comparing with pure spectra or the pattern of known concentrations.
In this case though, it holds that the concentrations and scores will be ordered identically due to the way that the N-way toolbox PARAFAC algorithm orders the components.
[TrpConcEst y(:,1)] to compare the estimated and reference concentrations.