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Parallel Computation of Bivariate Point Location Depths and Display of Intrinsic Contour Depth Elements
When: 11:00AM - 12:30PM , August 15, 2019
Speaker: Jane Holly DeBlois
Data depth is a central topic in order statistics and data analysis. However, the increasing needs of massive datasets and the related high costs of running algorithms pose challenges for statisticians and data analysts.
First, this thesis presents a new way to compute simplicial and Tukey data depths using Open Multi-Processing parallelization. We show that it is practical to compute point depths for tens of thousands of points. The definition of point depth is the order statistic depth of a single point, here in two dimensions.
Second, using the point depths, we explore the regional depth characteristics of the dataset as a whole. Using this new methodology, fast parallel computation of both simplicial depth and Tukey depth for a dataset of n points has time complexity O(n 2 log n) with O(n) space, which is practical for n up to 100,000.
Obtaining depths for a large number of points in a faster manner by parallel computation supports identifying the central region quickly, since the points of maximum depth are known. The point depth computation identifies the depths of selected spoke segments around each origin point. These spoke depths are used to create new visualizations of depth characteristics and contour depths without adding virtual points.
Directed By: Prof. Ming Ouyang