DOI

10.17077/etd.g6rgv6rs

Document Type

Dissertation

Date of Degree

Summer 2018

Access Restrictions

Access restricted until 08/31/2020

Degree Name

PhD (Doctor of Philosophy)

Degree In

Statistics

First Advisor

Kung-Sik Chan

First Committee Member

Johannes Ledolter

Second Committee Member

Aixin Tan

Third Committee Member

Tianbao Yang

Fourth Committee Member

Dale Zimmerman

Abstract

In this era of big data, multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. However, there have been limited studies of building a capable classifier with MTS via classical machine learning methods that can deal with the double curse of dimensionality due to high variable dimension and long time series (large sample size). In this thesis, we propose two approaches to address this problem for multiclass classification with high dimensional MTS.

Both approaches leverage the dynamics of an MTS captured by non-parametric modeling of its spectral density function. In the first approach, we introduce the reduced-rank spectral classifier (RRSC), which utilizes low-rank estimation and some new discrimination functions. We illustrate the efficacy of the RRSC with both simulations and real applications. For binary classification, we establish the consistency of the RRSC and provide an asymptotic formula for the misclassification error rates, under some regularity conditions. The second approach concerns the development of the random projection ensemble classifier for time series (RPECTS). This method first applies dimension reduction in the time domain via projecting the time-series variables into some low dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space.

We assess the classification performance of our new approaches by simulations and compare them with some existing methods using real applications. Finally, we elaborate two R packages that implement the aforementioned methods.

Keywords

classification, multivariate time series, random projection, reduced rank, spectrum

Pages

x, 127 pages

Bibliography

Includes bibliographical references (pages 124-127).

Copyright

Copyright © 2018 Fuli Zhang

Available for download on Monday, August 31, 2020

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