Filament estimation and uncertainty measures


Yen-Chi Chen

11:30:00 - 14:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Filamentary structure is a feature in multivariate data. It characterizes the local high density 1-dimensional manifold structure though there's no a strict definition of density filament. It arises from the astronomical data but has wide application to other fields such as medical image, computer vision and spatial statistics. A typical way to estimate filament from point cloud data is through kernel density reconstruction. However, it's hard to evaluate the uncertainty of filament since filaments are sets rather than single points. In this talk we'll briefly discuss a technique called subspace constrainted mean shift(SCMS) algorithm to estimate density ridge which is one way to define filament. And we will provide a way to define uncertainty measures of filament both locally and globally through distance function and metric. Then we'll introduce a boostrapping-based method to estimate this uncertainty measure and show that there's good visualization for this uncertainty measures in 2,3-dimensional data which is common in spatial-related problem. References: Nonparametric ridge estimation (2012) and The geometry of nonparametric filament estimation by Christopher R. Genovese, C.R., Perone-Pacifico, M., Verdinelli, I and Wasserman, L.