Graduation Year

2016

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody M. Ramachandran, Ph.D.

Committee Member

Dan Shen, Ph.D.

Committee Member

Lu Lu, Ph.D.

Keywords

Artificial Neural Networks, Feature Selection, Random Forests, Self-organizing Maps

Abstract

The Time Dependent Kernel Density Estimation (TDKDE) developed by Harvey & Oryshchenko (2012) is a kernel density estimation adjusted by the Exponentially Weighted Moving Average (EWMA) weighting scheme. The Maximum Likelihood Estimation (MLE) procedure for estimating the parameters proposed by Harvey & Oryshchenko (2012) is easy to apply but has two inherent problems. In this study, we evaluate the performances of the probability density estimation in terms of the uniformity of Probability Integral Transforms (PITs) on various kernel functions combined with different preset numbers. Furthermore, we develop a new estimation algorithm which can be conducted using Artificial Neural Networks to eliminate the inherent problems with the MLE method and to improve the estimation performance as well.

Based on the new estimation algorithm, we develop the TDKDE-based Random Forests time series classification algorithm which is significantly superior to the commonly used statistical feature-based Random Forests method as well as the Ker- nel Density Estimation (KDE)-based Random Forests approach.

Furthermore, the proposed TDKDE-based Self-organizing Map (SOM) clustering algorithm is demonstrated to be superior to the widely used Discrete-Wavelet- Transform (DWT)-based SOM method in terms of the Adjusted Rand Index (ARI).

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