Date of Award

Winter 12-2018

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Master of Arts (AM/MA)

Degree Type

Thesis

Abstract

Inspired by classic cocktail-party problem, the basic Independent Component Analysis (ICA) model is created. What differs Independent Component Analysis (ICA) from other kinds of analysis is the intrinsic non-Gaussian assumption of the data. Several approaches are proposed based on maximizing the non-Gaussianity of the data, which is measured by kurtosis, mutual information, and others. With each estimation, we need to optimize the functions of expectations of non-quadratic functions since it can help us to access the higher-order statistics of non-Gaussian part of the data. In this thesis, our goal is to review the one of the most efficient estimation methods, that is, the Fast Fixed-Point Independent Component Analysis (FastICA) algorithm, illustrate it with some examples using an R package.

Language

English (en)

Chair and Committee

John E. McCarthy

Committee Members

Jose E. Figueroa-Lopez; Jimin Ding

Fig1.png (31 kB)
Example 1

Fig2.png (63 kB)
Example 2

fig3.png (201 kB)
R result 1

fig4.png (347 kB)
R result 2

fig5.png (234 kB)
R result 3

ICAr2.pdf (976 kB)
R code (knitted)

Thesis(edited).pdf (1049 kB)

Share

COinS