Eigenvector and logarithmic least squares

The eigenvector method deals with two questions simultaneously, closeness and order. Together, they belong to the field topology of order. The metric idea of closeness is inadequate to judge what is a good approximation to data involving order relations. There is usually a condition which relates order in the derived scale to order in the data. This is precisely the kind of condition captured by the eigenvector, but not by the logarithmic least squares estimate.