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Navigating the World Through a Labeled Graph

Written by Taylor Le | Edited by Alexander Alva

Photo by Pixabay

After a brief helicopter ride around Mount Fuji, you stand at its base with aspirations to ascend it by nightfall. As the hike continues, cell reception gets weaker until GPS is unsustainable. With paper maps, you consider how to navigate the remaining trail: What is the optimal path to avoid getting lost and get there in record time? Have you considered the topology and connections of the trails? Understanding our movements – starting location, trajectory, ending location – is critical for our survival [1]. Two of many questions asked by neuroscientists studying spatial navigation are: How do people navigate the world? What and how are different navigational-based properties – including route, graph, labeled graph, and survey knowledge – and strategies used?

Route knowledge involves place-action associations (e.g., at the red light ahead, turn left) and relies on traveling on previously learned paths; it is insufficient, then, to explain novel routes and shortcut-taking. Route knowledge is non-metric, meaning that absolute distances and angles are not considered when navigating [2]. Topological knowledge relies on understanding the connectivity of the environment (e.g., a subway map), whereby each intersection represents a decision-making point (node) connected by paths (edges). Such edges and nodes can be used in route knowledge to create novel routes, but its non-metric properties make shortcuts impossible to plan [3]. On the other hand, survey knowledge can be thought of as a cognitive map, where objects and locations exist in an Euclidean (geometric) environment. Angles and absolute distances are consistent from any perspective and location, making survey knowledge highly flexible and, likely, the starting point for shortcut-formation [4]. 

Recent studies have examined the idea of a labeled graph, an intermediate property that links topological and survey knowledge. The labeled graph hypothesis may be the stage at which novel shortcuts are taken by incorporating the connectivity with somewhat limited map-like information of the environment. Chrastil and Warren’s 2014 study offers the first empirical evidence for use of a labeled graph by examining human navigational patterns. In an exploration phase, participants used immersive virtual reality to learn a maze environment with several objects. In the subsequent testing phase, the objects disappeared and subjects were asked to navigate the maze from one object to another based on their location in the exploration phase. Most participants preferentially took the shortest path between objects, which had not been taken during learning, suggesting shortcut-taking was utilized. Yet, in another testing phase where both the maze walls and objects disappeared, only 10% of participants were able to take a straight-line path from one object to another [5]. Similar results were found in Warren et. al.’s 2017 study, where participants readily took novel routes and shortcuts in an environment with wormholes that acted like teleporters, transporting and rotating from one location to another [6]. Both studies suggest the use of the labeled graph when learning one’s environment, since novel routes and shortcuts were observed without requiring a highly proficient understanding of survey knowledge. 

Overall, these studies and many more have offered further insight into the idea that spatial navigation is best denoted as a labeled graph. Currently, virtual reality experiments in controlled environments may have somewhat limited applicability to the real-world, and future studies may try to conduct studies in more real-life environments to emulate day-to-day navigation.

References:

1. “Spatial Knowledge.” ScienceDirect, https://www.sciencedirect.com/topics/computer-science/spatial-knowledge. Accessed 28 July 2022.

2. “Route Knowledge.” ScienceDirect, https://www.sciencedirect.com/topics/computer-science/route-knowledge. Accessed 28 July 2022.

3. Kim, K., Bock, O. (2021). Acquisition of Landmark, route, and survey knowledge in a wayfinding task: In stages or in parallel? – psychological research. SpringerLink

4. Johnson, C. (2018). Topological mapping and navigation in real-world environments. Deep Blue Repositories

5. Chrastil, E. R., Warren, W. H. (2014). From cognitive maps to cognitive graphs. PloS one, 9(11), e112544. 

6. Warren, W. H., Rothman, D. B., Schnapp, B. H., Ericson, J. D. (2017). Wormholes in virtual space: From cognitive maps to cognitive graphs. Cognition, 166:152–163. 

Published in Global Research

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