## Keywords

perceptual spaces, visual texture

## Abstract

Perceptual spaces are mental workspaces that organize a sensory or cognitive domain into a format that supports functions such as comparison, grouping, learning, and generalization. Determining the geometry of a perceptual space – i.e., the properties of the perceptual distances within the space -- is thus crucial not only to understand these intermediate levels of processing at an algorithmic level, but also as a starting point for comparison with neural measures of similarity. While perceptual spaces are often taken to be Euclidean or nearly so (the classic example is trichromatic color space), this assumption, when tested, is often violated. Moreover, entirely different geometries, such as distances on trees, may be more appropriate models for perceptual spaces with semantic content.

Here, rather than starting with a Euclidean model and asking whether adjustments need to be made, I take a complementary approach of identifying inferences that can be made directly from triadic judgments (is X or Y more similar to Z?). Each such judgment yields a ranking of distances but not a numerical relationship between them. Nevertheless, the set of rankings constrains models of the perceptual space. In particular, it yields indices of three geometrical characteristics: (i) consistency with symmetry; (ii) consistency with an “ultrametric” model (i.e., a strict hierarchy); and (iii) consistency with an “addtree” model (a graph-distance model, proposed by Tversky et al.). I provide examples from texture- and face-comparison experiments and outline some directions for further progress.

## Start Date

15-5-2024 2:00 PM

## End Date

15-5-2024 3:30 PM

## Location

ModVis 2024, St. Petersburg, FL

Characterization of perceptual spaces from triadic similarity judgments

ModVis 2024, St. Petersburg, FL

Perceptual spaces are mental workspaces that organize a sensory or cognitive domain into a format that supports functions such as comparison, grouping, learning, and generalization. Determining the geometry of a perceptual space – i.e., the properties of the perceptual distances within the space -- is thus crucial not only to understand these intermediate levels of processing at an algorithmic level, but also as a starting point for comparison with neural measures of similarity. While perceptual spaces are often taken to be Euclidean or nearly so (the classic example is trichromatic color space), this assumption, when tested, is often violated. Moreover, entirely different geometries, such as distances on trees, may be more appropriate models for perceptual spaces with semantic content.

Here, rather than starting with a Euclidean model and asking whether adjustments need to be made, I take a complementary approach of identifying inferences that can be made directly from triadic judgments (is X or Y more similar to Z?). Each such judgment yields a ranking of distances but not a numerical relationship between them. Nevertheless, the set of rankings constrains models of the perceptual space. In particular, it yields indices of three geometrical characteristics: (i) consistency with symmetry; (ii) consistency with an “ultrametric” model (i.e., a strict hierarchy); and (iii) consistency with an “addtree” model (a graph-distance model, proposed by Tversky et al.). I provide examples from texture- and face-comparison experiments and outline some directions for further progress.