Clustering Analysis for Non-Stationary Time Series
Gao, Bing
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Permalink
https://hdl.handle.net/2142/87405
Description
Title
Clustering Analysis for Non-Stationary Time Series
Author(s)
Gao, Bing
Issue Date
2006
Doctoral Committee Chair(s)
Hernando Ombao
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
The classical approaches to clustering are hierarchical and k-means. They are popular in practice. However, they can not address the issue of determining the number of clusters within the data. In this dissertation, we develop a best model-based clustering algorithm that can automatically select the best features for clustering, and estimate the number of clusters. The whole procedure can be divided into 2 steps. The first step is to find a basis from the WPs library that can best illuminate the difference among groups of the time series. The basis selected will consist of T WP functions, many of them irrelevant for discriminating/clustering groups. Thus, in the second step, we use the model-based variable selection algorithm to select the WPs that are really useful for clustering from the basis chosen in the first step. Redo the above 2 steps for each G from 2 to a preselect maximum number of clusters. Finally compare the models selected for each G by BIC. The best model contains information about the number of clusters and cluster membership. Moreover, based on best G, and the best WPs selected from the best basis, the EM result provides a measure of uncertainty about the associated classification of each time series. Simulation studies have been carried out and demonstrated that our method works well. We have also applied the method to a seismic data set, cluster the signals as earthquakes or explosions, and to epileptic seizure EEG data, separate the signals before and during epileptic seizure.
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