Non-metric multidimensional scaling

Non-metric MDS has been used extensively in the psychometrics and psychophysics communities to embed similarity and dissimilarity ratings derived from a variety of sources. Metric MDS is not appropriate in many of these applications since the magnitude of the input dissimilarities is unreliable, too difficult to measure, or simply unavailable.

 As a concrete example, suppose we wish to asses the perceptual similarity of some visual stimuli. We could ask human subjects to rate the similarity of these objects on a scale from one to a hundred, then embed these similarity ratings to visualize them. Unfortunately, different users will likely use different internal scales to asses similarity. Moreover, because of drift effects, a subject will sometimes rate a single stimulus differently depending on the order in which the stimuli where presented. Thus, the actual numbers that the users give are typically not reliable; however, the relative ordering of them will be fairly consistent. Because of the inconsistency of user ratings, non-metric MDS is more appropriate in this setting than metric MDS.