What if we do not have data to represent the pure classes?

If there are no sites fully covered by a single pure class, the statistical moments of the pure classes have to be inferred. It will be necessary then to use training data, i.e. data for which we know the mixing proportions by ground inspection. The set of linear mixing equations then

will have to be solved for the calculation of , and  which are the mean reflectances of the three pure classes in band j. In (13)  ,  and are the mean reflectances of 3 different mixed sites with mixing proportions, (a,b), (, ) and (, ) respectively. The more such training sites are available, the better the estimates of , and  will be: They will be obtained as the least square error solution of a system of equations like (13). A similar system of equations will have to be solved for the elements of the covariance matrices of the pure classes, and so on.