Date Approved

9-23-2024

Embargo Period

9-24-2024

Document Type

Thesis

Degree Name

Master of Arts (M.A.)

Department

Mathematics

College

College of Science & Mathematics

Advisor

Nasrine Bendjilali, Ph.D.

Committee Member 1

Thanh Nguyen, Ph.D.

Committee Member 2

Olcay Ilicasu, Ph.D.

Keywords

deep learning; K-Means clustering; kernel principal component analysis; multilayer perceptron; neural networks; principal component analysis

Subject(s)

Neural networks (Computer Science); Computer architecture

Disciplines

Applied Mathematics | Computer Sciences

Abstract

Neural networks have proven to be powerful tools for modeling a wide range of problems across applications. However, one of the challenges in implementing a neural network model lies in determining the neural network architecture, i.e. the appropriate number of hidden layers and the number of neurons per hidden layer. It has been suggested that one way to determine the number of hidden layers is by using information on the variability captured by each principal component. In this research, we expand on this idea and propose a new approach to determine the neural network architecture for a multilayer perceptron used to classify data with a large number of attributes. The proposed approach makes use of kernel principal component analysis and clustering to determine the appropriate number of hidden layers and neurons per hidden layer. This methodology was tested using two datasets: the Parkinson’s Disease Classification dataset with binary outcomes, and the Gas Sensor Array Drift dataset with six output classes. The application of the proposed method suggests a three-hidden-layer architecture for the Parkinson’s Disease Classification dataset, achieving an average validation accuracy of 89%, while a two-hidden-layer architecture is recommended for classifying the Gas Sensor Array Drift dataset, achieving an average validation accuracy of 98%. Performance comparisons between various models and architectures are presented.

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