Women in Mathematics Talks

Getting Your Computer Into Shape: Modeling Objects in Two and Three Dimensions

Friday, February 11, 2022

Kathryn Leonard’s research interests are in geometric modeling with applications to computer vision, computer graphics, and data science. Her work has been recognized with a CAREER award from NSF, the Henry L. Alder Award for Excellence in Teaching from the MAA, and a Service Award from the Association of Women in Mathematics (AWM). She became a math major in her junior year of college, after her petition to waive the university’s math GE requirement was rejected. Currently, she is President of AWM. She also directs the NSF-funded Center for Undergraduate Research in Mathematics, leads the AWM research networks for Women in Shape and Women in the Data Science and Mathematics, and is on the Board of Directors of Steam:Coders, a local non-profit working to make computing education accessible to all. She has held positions at CSU Channel Islands, where she helped build a university, Caltech, and MSRI, and is currently at Occidental College. She still gets no respect from her cat.

Abstract

Shape understanding—looking at a shape and intuitively understanding which parts are, e.g., body, arms, legs, toes, and ears—is almost effortless for humans. Training a computer to understand shapes in a similar way, however, presents substantial challenges. This talk will discuss human shape perception and the challenges of automation. We will describe a useful mathematical shape model, the Blum medial axis (BMA), and a method based on the BMA for automatically decomposing a shape into a hierarchy of parts and determining the similarity between those parts. We compare our automated results to human perception data gathered from a massive user study, and also provide some useful applications. Time permitting, we will present recent work and an open annual challenge to use neural networks to learn the BMA from input images. We’ll also share personal stories of how we ended up doing this work.

Compressed Anomaly Detection with Multiple Mixed Observations

Friday, Oct. 29, 2021

Natalie Durgin ’09 is a Research Staff Member at the Center for Communications Research in La Jolla, CA. Previously she worked as a Senior Data Scientist at Spiceworks, an Austin tech company. During her four-year tenure, she built a diverse set of statistical and machine learning models for prediction, classification, optimization, and natural language processing. She earned a Ph.D. in mathematics at Rice University, where she studied Algebraic Geometry and Geometric Invariant Theory. After hours, she enjoys rock climbing, cooking, and solving the “Monday Punday”.

Abstract

Nowadays, data is pouring in from all directions. Whether it emanates from financial markets or agricultural soil sensors, we can think of each data feature as a random variable with a probability distribution. Suppose we have an enormous collection of independent random variables that are identically distributed except for a few anomalies. How can we efficiently detect these anomalies without copiously sampling each of the random variables and conducting individual hypothesis tests? Recent work* proposes to ease the pain by conducting hypothesis tests based on mixed observations (e.g. linear combinations) of the random variables. In this talk, we will relate this mixed observation scenario to the compressed sensing concept of multiple measurement vectors (MMVs). Many algorithms have been developed for recovering jointly sparse signals and their support from MMVs. We will establish the theoretical and empirical effectiveness of some of these existing algorithms at detecting anomalous random variables.