Abstract: Many geometric and topological methods rely on the metric information of input data. In this talk, I will explore three natural setups for modeling noise associated with input data/metric. Specifically, (i) the input data could already be embedded in a metric space, but the embedding may be noisy; or (ii) we are given a noisy discrete n-point metric as input which could include outliers; and we aim to remove these outliers and embed remaining points to a target metric space with low distortion; or (iii) the target metric is induced from an input graph which itself is noisy, leading to noisy graph metrics. I will describe the specific noise model in each setup and present denoising approaches for each case to recover the metric information with theoretical guarantees. Our methods draw ideas from computational geometry, theoretical computer science and statistical modeling.
Brief Bio: Yusu Wang is Associate Professor of Computer Science and Engineering Department at the Ohio State University. She obtained her PhD degree from Duke University, where she received the Best PhD Dissertation Award at CS Dept., Duke U, in 2004. Before joining OSU in 2005, she was a post-doctoral fellow at Stanford University from 2004--2005. Yusu Wang works in the fields of Computational geometry and Computational topology. She is primarily interested in developing effective and theoretically justified algorithms for data / shape analysis using geometric and topological ideas and methods, and in applying them to practical domains, including computational biology, computer graphics and visualization. She received DOE Early Career Principal Investigator Award in 2006, NSF Career Award in 2008, and several best paper awards, including the Best Paper award in SIGSPATIAL GIS 2015 and the Mark Fulk Best Student Paper award in COLT 2015.