Bibliographic Details
| Title: |
Metric information in cognitive maps: Euclidean embedding of non-Euclidean environments. |
| Authors: |
Baumann, Tristan1 (AUTHOR) tristan.baumann@tuebingen.mpg.de, Mallot, Hanspeter A.2 (AUTHOR) |
| Superior Title: |
PLoS Computational Biology. 12/27/2023, Vol. 19 Issue 12, p1-14. 14p. |
| Subject Terms: |
*COGNITIVE maps (Psychology), *EUCLIDEAN metric, *METRIC spaces, *GRAPH labelings, *HUMAN behavior, *TIME measurements |
| Abstract: |
The structure of the internal representation of surrounding space, the so-called cognitive map, has long been debated. A Euclidean metric map is the most straight-forward hypothesis, but human navigation has been shown to systematically deviate from the Euclidean ground truth. Vector navigation based on non-metric models can better explain the observed behavior, but also discards useful geometric properties such as fast shortcut estimation and cue integration. Here, we propose another alternative, a Euclidean metric map that is systematically distorted to account for the observed behavior. The map is found by embedding the non-metric model, a labeled graph, into 2D Euclidean coordinates. We compared these two models using data from a human behavioral study where participants had to learn and navigate a non-Euclidean maze (i.e., with wormholes) and perform direct shortcuts between different locations. Even though the Euclidean embedding cannot correctly represent the non-Euclidean environment, both models predicted the data equally well. We argue that the embedding naturally arises from integrating the local position information into a metric framework, which makes the model more powerful and robust than the non-metric alternative. It may therefore be a better model for the human cognitive map. Author summary: How is the metric of space, i.e., knowledge about distances and angles between places, represented in the brain? Existing theories argue for either purely relational topological graphs without a metric, or consistent Euclidean maps where each place is assigned specific coordinates. The problem lies in the fact that human behavior systematically deviates from perfect metric maps, and theories need to account for these deviations. We propose an intermediate model that has both properties of non-metric graphs and metric maps, by embedding a graph labeled with local position information into metric space. In this "embedded graph", measurements of local metric information also affect the estimates of adjacent distances and turning angles. The result is a consolidated spatial representation which is still a graph, but whose local metric labels are globally optimized to match the available egomotion measurements. We show that the embedded graph is consistent with human behavior in a (virtual) non-Euclidean environment and argue that it is a natural consequence of the optimal integration of repeated local measurements over time. [ABSTRACT FROM AUTHOR] |
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