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ArXiv
ArXiv
arxiv
ArXiv
2331-8422
Cornell University

arXiv:2310.07543v2
2310.07543
2
preprint
Article
Ordinal Characterization of Similarity Judgments
Victor Jonathan D.
Aguilar Guillermo
Waraich Suniyya A.
5 9 2024
arXiv:2310.07543v211 10 2023
https://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License, which allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
http://arxiv.org/abs/2310.07543v2
nihpp-2310.07543v2.pdf
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 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 indices that characterize the set of judgments in three ways: compatibility with a symmetric dis-similarity, compatibility with an ultrametric space, and compatibility with an additive tree. Each of the indices is derived from rank-order relationships among the choice probabilities that, as we show, are necessary and sufficient for local consistency with the three respective characteristics. We illustrate this approach with simulations and example psychophysical datasets of dis-similarity judgments in several visual domains and provide code that implements the analyses at https://github.com/jvlab/simrank.

Body: 64 pages; 16 figures; 7 supplementary figures, 3 appendices. This replacement is a major revision in response to peer reviews in Mathematical Neuroscience and Applications (MNA). Main changes are (i) reorganization to separate theory and implementation, (ii) addition of analyses of synthetic datasets, (iii) expanded discussion of alternatives and open issues
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