December 2022
Volume 22, Issue 14
Open Access
Vision Sciences Society Annual Meeting Abstract  |   December 2022
Estimating the perceived dimensionality of psychophysical stimuli using a triplet accuracy and hypothesis testing procedure
Author Affiliations & Notes
  • David-Elias Künstle
    University of Tübingen
    International Max Planck Research School for Intelligent Systems, Tübingen
  • Ulrike von Luxburg
    University of Tübingen
    Max Planck Institute for Intelligent Systems, Tübingen
  • Felix A. Wichmann
    University of Tübingen
  • Footnotes
    Acknowledgements  This work has been supported by the Machine Learning Cluster of Excellence, funded by EXC number 2064/1 – Project number 390727645. The authors would like to thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting David-Elias Künstle.
Journal of Vision December 2022, Vol.22, 3331. doi:
  • Views
  • Share
  • Tools
    • Alerts
      This feature is available to authenticated users only.
      Sign In or Create an Account ×
    • Get Citation

      David-Elias Künstle, Ulrike von Luxburg, Felix A. Wichmann; Estimating the perceived dimensionality of psychophysical stimuli using a triplet accuracy and hypothesis testing procedure. Journal of Vision 2022;22(14):3331.

      Download citation file:

      © ARVO (1962-2015); The Authors (2016-present)

  • Supplements

In vision research we are often interested in understanding the mapping of complex physical stimuli to their perceptual dimensions. This mapping can be explored experimentally with multi-dimensional psychophysical scaling. One fruitful approach is the combination of triplet comparison judgments, asking if stimulus A or B is more similar to C, together with ordinal embedding methods. Ordinal embedding infers a point representation such that the distances in the inferred, internal perceptual space agree with the observer’s judgments. One fundamental problem of psychophysical scaling in multiple dimensions is, however, that the inferred representation only reflects perception if it has the correct dimensionality. Unfortunately, the methods to derive the “correct” dimensionality were thus far not satisfactory for noisy, behavioural data (e.g. no clear “knee” in the stress-by-dimension graph of multi-dimensional scaling). Here we propose a statistical procedure inspired by model selection to choose the dimensionality: Dimensionality can be tuned to prevent both under- and overfitting. The key elements are, first, measuring the scale’s quality by the number of correctly predicted triplets (cross-validated triplet accuracy). Second, performing a statistical test to assess if adding another dimension improves triplet accuracy significantly. In order to validate this procedure we simulated noisy and sparse judgments and assessed how reliably the ground-truth dimensionality could be identified. Even for high noise levels we are able to identify a lower-bound estimate of the perceived dimensions. Furthermore, we studied the properties and limitations of our procedure using a variety of behavioural datasets from psychophysical experiments. We conclude that our procedure is a robust tool in the exploration of new perceptual spaces and is able to help identify a lower bound on the number of perceptual dimensions for a given dataset. The identified dimensions and the resulting representation can then be related to perceptual processes in order to explore human vision.


This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.