Data Depth for Non-Euclidean Objects (Xiongtao Dai -- Iowa State)

  • Starts: 4:00 pm on Thursday, January 27, 2022
  • Ends: 4:12 pm on Saturday, October 18, 2025
Non-Euclidean data objects such as directions, covariance matrices, and trees have been increasingly generated in modern practice. As an important first step, data analysts would like to explore the data distributions and identify typical versus extreme observations. Originally introduced for multivariate data, data depth is a powerful nonparametric tool to measure the centrality of an observation with respect to a distribution. Our work develops the metric halfspace depth, a data depth method applicable to objects lying on a general metric space, extending the well-known Tukey's depth for Euclidean data. We show that the metric halfspace depth enjoys intuitive interpretation and leads to a center-outward ranking useful for data exploration. In addition, inferential methods such as robust location estimation and rank tests can also be established. We will discuss desirable statistical properties and efficient computation for the metric halfspace depth. The proposed method was applied to reveal group differences in the brain connectivity patterns among Alzheimer's disease patients, and in a second application, to identify the consensus and outliers from a sample of phylogenetic trees for 7 pathogenic parasites.
Location:
Virtual -- email estephen@bu.edu to be added to the announcement list