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A quantum geometric framework for modeling color similarity judgments

Epping, G., Fisher, E., Zeleznikov-Johnston, A. , Pothos, E. M. ORCID: 0000-0003-1919-387X & Tsuchiya, N. (2023). A quantum geometric framework for modeling color similarity judgments. Cognitive Science, 47(1), article number e13231. doi: 10.1111/cogs.13231


Since Tversky (1977) argued that similarity judgments violate the three metric axioms, asymmetrical similarity judgments have been particularly challenging for standard, geometric models of similarity, such as multidimensional scaling. According to Tversky (1977), asymmetrical similarity judgments are driven by differences in salience or extent of knowledge. However, the notion of salience has been difficult to operationalize, especially for perceptual stimuli for which there are no apparent differences in extent of knowledge. To investigate similarity judgments between perceptual stimuli, across three experiments we collected data where individuals would rate the similarity of a pair of temporally separated color patches. We identified several violations of symmetry in the empirical results, which the conventional multidimensional scaling model cannot readily capture. Pothos et al. (2013) proposed a quantum geometric model of similarity to account for Tversky’s (1977) findings. In the present work, we extended this model to a more general framework that can be fit to similarity judgments. We fitted several variants of quantum and multidimensional scaling models to the behavioral data and concluded in favor of the quantum approach. Without further modifications of the model, the best-fit quantum model additionally predicted violations of the triangle inequality that we observed in the same data. Overall, by offering a different form of geometric representation, the quantum geometric framework of similarity provides a viable alternative to multidimensional scaling for modeling similarity judgments, while still allowing a convenient, spatial illustration of similarity.

Publication Type: Article
Additional Information: This is an accepted manuscript of an article published in Cognitive Science by Cognitive Science Society.
Publisher Keywords: similarity, asymmetrical judgments, triangle inequality, multidimensional scaling, geometric model of similarity, quantum cognition
Subjects: B Philosophy. Psychology. Religion > BF Psychology
Departments: School of Health & Psychological Sciences > Psychology
SWORD Depositor:
[thumbnail of Color_Similarity_Manuscript4.pdf]
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