Seminar | March 30 | 4-5 p.m. | 531 Cory Hall
Rob Nowak, UW Madison
Modeling human perceptions has many applications in cognitive, social, and educational science, as well as in advertising and commerce. I will discuss our ongoing work on ordinal embedding, also known as non-metric multidimensional scaling, which is the problem of representing items (e.g., images) as points in a low-dimensional Euclidean space given constraints of the form "item i is closer to item j than item k. In other words, the goal is to find a geometric representation of data that is faithful to comparative similarity judgments. This classic problem is often used to gauge and visualize perceptual similarities. A variety of algorithms exist for learning metric embeddings from comparison data, but the accuracy and performance of these methods were poorly understood. I will present a new theoretical framework that quantifies the accuracy of learned embeddings and indicates how many comparisons suffice as a function of the number of items and the dimension of the embedding. This theory also points to new algorithms that outperform previously proposed methods. I will also describe a few applications of ordinal embedding.
This is joint work with Lalit Jain, Kevin Jamieson, and Blake Mason.