Title: Branching out: New techniques in tree representations of time series with applications
Authors: Zoe Haskell - University of Nevada, Reno (United States) [presenting]
Ilya Zaliapin - University of Nevada Reno (United States)
Abstract: Tree representation of continuous functions has historically been used to explore the properties of trees and stochastic processes. However, its usage in an applied analysis of time series remains limited. We introduce new objects, partial trees and partial Harris paths, that facilitate mapping between finite time series and rooted plane trees, and establish correspondences between natural operations on trees and their time-series counterparts. We show that the Horton pruning of a tree (cutting leaves and subsequent series reduction) corresponds to taking the local minima of a time series. We also present new pruning algorithms adopted for the analysis of spiky time series and of series with significant flat periods (plateaus). We illustrate the proposed techniques in the problems of noise reduction via pruning in tree-space, and detecting clusters in sets of time series data, including work done at Disney for audience segmentation.