Paper on fuzzy rose diagrams lands top student paper award
In 2013, MU doctoral student Andrew Buck and James Keller, Curators’ Professor and the R.L. Tatum professor of electrical and computer engineering, won “Best Overall Paper” honors at the Institute of Electrical and Electronics Engineers (IEEE) Symposium Series on Computational Intelligence (SSCI).
In 2014, the duo teamed up to take their research on fuzzy diagrams in a different direction, but they achieved a similar result — “Best Student Paper” at the 2014 IEEE SSCI event in Orlando, Fla.
Buck and Keller’s work in 2013 focused on scene matching fuzzy descriptions with satellite imagery, mapping out possibilities for how a person in an unknown location could potentially use vague spatial ideas to navigate an area in which a person may only be able to recall hazy details.
The 2014 paper, “Visualizing Uncertainty with Fuzzy Rose Diagrams,” also used a directional example to illustrate how to diagram and account for the uncertainty of a wide swath of variables.
The example problem queried which route to take to get from one destination to another and why a person might select one over another. Example Route 1 went through the woods, had a slight elevation change, followed a dirt path, was shaded and involved crossing water. Example Route 2 went over a hill, allowing for the shortest total distance but the highest change in elevation, was in the sun and involved no water crossing. Example Route 3 was the longest distance, was paved and flat, was in the sun and involved no water crossing. Mathematical functions were used to determine the probability for variables such as distance, slope, path, shade and water to affect the decision of which path to choose.
“One person might like to go the fastest route or the most scenic route,” Keller said. “And the parameters that make you decide on that are not very precisely known.
“And in those cases, that uncertainty can be represented by many different forms, and the form that we like is this form called fuzzy sets.”
The goal was to visualize the parameters all in a single graph, allow for a high number of features, to be easy to read and digest and be reproducible. The duo opted to use rose diagrams, pioneered by Florence Nightingale, who used them to diagram causes of death of British soldiers and their allies in the Crimean War. Rose diagrams are similar to pie charts except that instead of making the angle of each wedge bigger or smaller depending on the value, the wedge’s radius expands or shrinks.
“What we looked at is how do you do that with fuzzy numbers?” Buck said. “We settled on what we call this fuzzy rose diagram.
“We have these shapes, these petals where the uncertainty is represented by the shape of the petal. So you can have a crisp value with no uncertainty or something right next to it where it could be any value.”
Petals that cover a wider range or are fatter toward the center of the graph correlate with less uncertainty; ones that are fatter at the top indicate greater uncertainty. The size and shape are computed using cumulative functions, turning them and taking their mirror image.
“You can actually aggregate all of these features along each of the decisions that you might take,” Buck said. “And at the bottom here, you have what is the end result of taking this action. If I choose to go through the path this way, what is the total amount of all of these features [that I’ll be dealing with].”
The work landed Buck and Keller another chance to shine among their peers in the computational intelligence industry. And while 2013’s was more anticipated, Buck said the idea for this project came about more by accident. The duo was working on a project for the National Geospatial-Intelligence Agency and needed a way to easily access and glance at the data. So they started working on a model, and it led to an award-winning paper.
“We said, ‘It’s too cool to not do something with,’” Keller said. “What’s interesting is this paper, while it came as sort of an accidental discovery, it really resonated with all of the referees. If you look at the reviews that came with this paper, every one was glowing. It was a nice, pleasant surprise.”