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Dynamic Update of Half-space Depth Contours
|Authors:||Burr, Michael A.; Rafalin, Eynat; Souvaine, Diane L.|
Data depth is a statistical analysis method that assigns a numeric value to each point, corresponding to its centrality relative to a data set. Depth contours, nested contours that enclose regions with increasing depth, provide a powerful method to visualize, quantify and compare data sets. We present the first dynamic algorithm for computing the half-space depth contours of a set of n points in R^2 in O(n log n) and O(n log^2 n) time per operation for two flavors of depth contours and in quadratic space, an improvement over the static version of O(n^2) time per operation. Our analysis characterizes key constraints on potential contour changes under insertion and deletion, that have not been identified before.
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