Title: Investigating the role of visual clustering in approximate numerosity perception
Date: December 12, 2024
Time: 1:30pm - 3:00pm ET
Location: online
Zoom Link: https://gatech.zoom.us/j/95965447145?pwd=C3yaFCFKzA6LFfAswIVNKrb7Uqoj2n.1
Vijay Marupudi
Ph.D. Student in Human-Centered Computing School of Interactive Computing College of Computing Georgia Institute of Technology
Committee:
Dr. Sashank Varma (Advisor), School of Interactive Computing, Georgia Institute of Technology Dr. Chris MacLellan, School of Interactive Computing, Georgia Institute of Technology Dr. Cindy Xiong Bearfield, School of Interactive Computing, Georgia Institute of Technology Dr. Elizabeth Brannon, Department of Psychology, University of Pennsylvania Dr. Priti Shah, Department of Psychology, University of Michigan
Abstract:
The ability to visually perceive distinct objects as groups that belong together is a core part of human perception. This ability, called visual clustering, is important for a wide range of human behaviors such as ensemble perception, visual working memory, spatial problem-solving, and understanding information visualizations. However, surprisingly little is known about this ability, which is also known as Gestalt proximity grouping. It is complex. From a computational perspective, for any given criterion --- for example minimizing the variance of the distances between objects within clusters and maximizing the variance of the distances between clusters --- we are not currently aware of an algorithm that can find an optimal solution efficiently, i.e., in polynomial time.
My proposal presents a series of completed works outlining the properties of human visual clustering. I presented participants with stimuli that varied in the number of points they contained and their statistical cluster structure (clustered points vs dispersed points). They were asked to cluster the points by drawing shapes around them. People's clusterings of the same stimuli at two different time points were remarkably similar to each other, with partipicants showing greater reliability for clustered stimuli with diminishing reliability with increasing number of points. People's clusterings were also highly similar to each other, and were consistent with a Gaussian distribution. These properties suggest that visual clustering may serve as a basis for other cognitive abilities.
To demonstrate this, I investigated whether people may use clustering to solve the traveling salesperson problem (TSP). People are unexpectedly performant at this task, staying within 10\% of optimal solutions and solving problems in time linear to the number of points. I asked participants to solve TSP problems at two different time points. I found that the reliability patterns of the TSP for clustered and dispersed stimuli followed the same patterns as visual clustering, implying that clustering may be used to solve the TSP. In a second experiment, I asked people to cluster and solve the TSP on the same stimuli and found that people's TSP solutions were remarkably consistent with their clusterings, with 52\% of TSP solutions being perfectly congruent with their clusterings. Even when their solutions weren't perfectly congruent, they displayed high amounts of congruency in general, providing further support to the theory that people use the clusters they perceive to solve the TSP.
Finally, I am proposing a series of experiments to investigate whether people are using visual clustering to judge visual numerosity. Past work on this topic has uncovered several illusions and effects where the potential grouping of points can result in people underestimating the numerosity of a set of points. Some of these include the connectedness illusion, the random-regular illusion, and the solitaire illusion. However, it is still unclear whether people perceive these groups of points while estimating numerosity, and whether the groups people perceive are responsible for the effects of the spatial arrangements of points on numerosity estimation. Additionally, perceiving groups of points in a set also introduces a competing numerosity cue, the number of groups in a set. The first experiment I will conduct will focus on investigating the random-regular illusion, where people view more clustered points as less numerous than more dispersed points. This will be done by asking people to compare and estimate the numerosity of sets of points that pit the statistical cluster structure against the numerosity of the sets. The second experiment will target the competing numerosity cue, and will pit the number of groups in a stimulus against the numerosity of the sets. Together, these experiments will systematically investigate the role of visual clustering on numerosity estimation and will examine the mechanisms that underlie our ability to quickly judge the numerosity of visual input, an ability critical to understanding and making good decisions and accurate inferences from information visualizations.