New article accepted for publication in the Journal of Vision
Title: "Estimation of perceptual scales using ordinal embedding" by Siavash Haghiri, Felix Wichman and Ulrike von Luxburg
In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments of the form: "Is stimulus Si more similar to stimulus Sj or to stimulus Sk?". We propose to use ordinal embedding methods from machine learning to estimate the scaling function from the relative judgments. We review two relevant and well-known methods in psychophysics that are partially applicable in our setting: non-metric multi-dimensional scaling (NMDS) and the method of maximum likelihood difference scaling (MLDS). Considering various scaling functions, we perform an extensive set of simulations to demonstrate the performance of the ordinal embedding methods. We show that in contrast to existing approaches our ordinal embedding approach allows, first, to obtain reasonable scaling functions from comparatively few relative judgments, and second, to estimate multi-dimensional perceptual scales. In addition to the simulations, we analyse data from two real psychophysics experiments using ordinal embedding methods. Our results show that in the one-dimensional perceptual scale our ordinal embedding approach works as well as MLDS, while in higher dimensions, only our ordinal embedding methods can produce a desirable scaling function. To make our methods widely accessible, we provide an R-implementation and general rules of thumb on how to use ordinal embedding in the context of psychophysics.