  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 S_i more similar to stimulus S_j or to
stimulus S_k?". 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 which are partially
applicable in our setting: non-metric multi-dimensional scaling (NMDS) and the
method of maximum likelihood difference scaling (MLDS). We perform an extensive
set of simulations, considering various scaling functions, 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 function from comparatively few relative judgments, second,
the estimation of non-monotonous scaling functions, and, third,
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, monotonically increasing
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.
