The more recent multi-arrangement method, ‘inverse MDS,’ circumvents many of these limitations and is very efficient 12. Free sorting (into any number of piles) is intuitive, but it forces the subject to categorize the stimuli, even if the stimuli do not easily lend themselves to categorization. Quicker alternatives, like sorting into a predefined number of clusters 11 or free sorting have their own limitations. While this would yield a more reliable rank ordering of dissimilarities, the number of comparisons required scales with the fourth power of the number of stimuli, making it feasible for only small stimulus sets. (Here, a context effect is defined as a change in the judged similarity between two stimuli, based on the presence of other stimuli that are not being compared.) Alternatively, subjects can be asked to compare all pairs of stimuli to all other pairs of stimuli. While this is relatively quick, estimates tend to be unstable across long sessions as subjects cannot go back to previous judgments, and context effects, if present, cannot be detected. The most straightforward way of obtaining quantitative measures of dissimilarity is to ask subjects to rate on a scale the degree of dissimilarity between each pair of stimuli. There are many methods for collecting similarity judgments, each with its advantages and disadvantages. These pairwise dissimilarities (or perceptual ‘distances’) can then be used to model the perceptual space via multidimensional scaling 10. From similarity judgments, one can obtain quantitative estimates of dissimilarities. Applied to sensory domains, this kind of model is often referred to as a ‘perceptual space 9.’ Points in the space represent stimuli and distances between points correspond to the perceived dissimilarity between them. Thus, similarity judgments provide valuable insight into information-processing in the brain.Ī common model of mental representations using similarities is a geometric space model 6– 8. Studying how mental representations change during development can shed light on how they are learned 5. Additionally, similarity judgments reveal features that are salient in perception 4. It is also possible to gain insight into neural computations, by relating similarity judgments to brain activation patterns 3. Understanding the structure of mental representations can provide insight into the organization of conceptual knowledge 2. Similarity judgments are commonly used to probe these mental representations 1. Humans mentally process and represent incoming sensory information to perform a wide range of tasks, such as object recognition, navigation, making inferences about the environment, and many others. Each trial yields the results of 28 pairwise comparisons of the form, “Was A more similar to the reference than B was to the reference?” While directly comparing all pairs of pairs of stimuli would have required 221445 trials, this design enables reconstruction of the perceptual space from 5994 such comparisons obtained from 222 trials. The approach is illustrated with an experiment measuring similarities among 37 words. The approach was validated for stimuli drawn from Euclidean spaces of up to 5 dimensions. By judicious selection of combinations of stimuli used in each trial, the approach has internal controls for consistency and context effects. Typical trials consist of 8 stimuli around a central reference stimulus: the subject ranks stimuli in order of their similarity to the reference. Here, a novel ranking paradigm for efficient collection of similarity judgments is presented, along with an analysis pipeline (software provided) that tests whether Euclidean distance models account for the data. This is much more efficient (the number of ratings grows quadratically with set size rather than quartically), but these ratings tend to be unstable and have limited resolution, and the approach also assumes that there are no context effects. An alternative strategy is to ask a subject to rate similarities of isolated pairs, e.g., on a Likert scale. For example, if one asks a subject to compare the similarity of two items with the similarity of two other items, the number of comparisons grows with the fourth power of the stimulus set size. Ideally, one might want to compare estimates of perceived similarity between all pairs of stimuli, but this is often impractical. This approach has been used to characterize perceptual spaces in many domains: colors, objects, images, words, and sounds. Similarity judgments are commonly used to study mental representations and their neural correlates.
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