A1066
Title: Tukey's depth for object data
Authors: Xiongtao Dai - University of California, Berkeley (United States)
Sara Lopez Pintado - Northeastern University (United States) [presenting]
Abstract: A novel exploratory tool for non-Euclidean object data is developed based on data depth, extending celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in general metric spaces, assigns to data points depth values that characterize the centrality of these points concerning the distribution and provides an interpretable centre-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor in theory and simulation. An efficient algorithm is proposed to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimer's disease study, revealing group differences in brain connectivity, modelled as covariance matrices, for subjects in different stages of dementia.
