A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

The Geometry of Low- and High-Level Perceptual Spaces

Low-level features are typically continuous (e.g., the gamut between two colors), but semantic information is often categorical (there is no corresponding gradient between dog and turtle) and hierarchical (animals live in land, water, or air). To determine the impact of these differences on cognitive representations, we characterized the geometry of perceptual spaces of five domains: a domain dominated by semantic information (animal names presented as words), a domain dominated by low-level features (colored textures), and three intermediate domains (animal images, lightly texturized animal images that were easy to recognize, and heavily texturized animal images that were difficult to recognize). Each domain had 37 stimuli derived from the same animal names. From 13 participants (9F), we gathered similarity judgments in each domain via an efficient psychophysical ranking paradigm. We then built geometric models of each domain for each participant, in which distances between stimuli accounted for participants' similarity judgments and intrinsic uncertainty. Remarkably, the five domains had similar global properties: each required 5-7 dimensions, and a modest amount of spherical curvature provided the best fit. However, the arrangement of the stimuli within these embeddings depended on the level of semantic information: dendrograms derived from semantic domains (word, image, and lightly texturized images) were more "tree-like" than those from feature-dominated domains (heavily texturized images and textures). Thus, the perceptual spaces of domains along this feature-dominated to semantic-dominated gradient shift to a tree-like organization when semantic information dominates, while retaining a similar global geometry.

Ordinal Characterization of Similarity Judgments

Characterizing judgments of similarity within a perceptual or semantic domain, and making inferences about the underlying structure of this domain from these judgments, has an increasingly important role in cognitive and systems neuroscience. We present a new framework for this purpose that makes very limited assumptions about how perceptual distances are converted into similarity judgments. The approach starts from a dataset of empirical judgments of relative similarities: the fraction of times that a subject chooses one of two comparison stimuli to be more similar to a reference stimulus. These empirical judgments provide Bayesian estimates of underling choice probabilities. From these estimates, we derive three indices that characterize the set of judgments, measuring consistency with a symmetric dis-similarity, consistency with an ultrametric space, and consistency with an additive tree. We illustrate this approach with example psychophysical datasets of dis-similarity judgments in several visual domains and provide code that implements the analyses.