Monotone mapping of similarities into a general metric space

A method of “maximum variance nondimensional scaling” is described and tested that transforms similarity measures into distances that meet just three conditions: (C1) they exactly satisfy the metric axioms, (C2) they are, as nearly as possible, monotonically related to the similarity measures, (C3) they have maximum variance possible under the two preceding conditions. By achieving an appropriate balance between the last two conditions, one can determine the true underlying distances and the form of the unknown monotone function relating the similarity measures to those distances without assuming that the underlying space has any particular Euclidean, Minkowskian, or even dimensional strucutre. The method appears to have potential applications, e.g., to studies of stimulus generalization and the structure and processing of semantic information.