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 know that the concentration of tryptophan in the
fifth sample is y(5,1). 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
> TrpConcEst = A(:,1)/A(5,1)*y(5,1);
the 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.