Metric information in cognitive maps: Euclidean embedding of non-Euclidean environments
Fig 4
(a, b) References for comparison. The unembedded graph (as in Fig 2) and an another embedding which was also found by the optimization method. The second embedding performed worse on the subject data and was not further used. (b) The embedded graph, i.e., the labeled graph with the vertices at coordinates that minimize the difference between map and labels. The orientation of the embeddings is arbitrary; here, they were rotated so that the edge (2, 3) is horizontal. The red dotted lines show the edges that pass through wormholes. (d) Sketch of the distorted wormhole maze according to the embedding in (c). The sketch shows how the embedding might be represented by a subject. Edges that cross each other in the embedded graph could for example be rationalized as multi-level paths, leading to a 3D representation. Alternatively, in a purely 2D map, the arms would simply intersect. Note that the edges have no coordinates in the embedding but are simply lines in the adjacency matrix.