Hierarchical analysis: Classification with ordinal object dissimilarities

Summary Lerman 1970] has demonstrated, that the dissimilarity indices normally used in data analysis are identical up to strictly monotone transformationsf:R ₊R ₊ if the data are nominal and each set of attribute scores is finite.In that case he proposes to use a preorder between pairs of objects to express similarity or dissimilarity, in order to avoid inconsistent classification results that might occur, if clustering schemes which are not monotone invariant are applied to a quantitative index. Here it is shown, how a hierarchy on the objects can be calculated if such a preorder relation is given.