Optimization and Machine Learning Techniques for Analyzing Spatiotemporal Dynamics

Authors

• Dipak Prasad Dulal, University of Alabama at Birmingham

Advisor(s)

Carmeliza Navasca

Committee Member(s)

Chengcui Zhang
Junfang Li
Shan Zhao
Sivaguru Ravindran

School

College of Arts and Sciences

Document Type

Dissertation

Department (new version)

Natural Sciences & Mathematics

Date of Award

9-9-2024

Abstract

In a numerical context, the tensor CP decomposition challenge can be reformulated into a series of least squares subproblems, which can be addressed using the renowned Alternating Least Square algorithm (ALS). The ALS algorithm is often characterized by a 'swamp phenomenon' that slows down its convergence, especially when dealing with extensive data structures. One of the goals of our research is to find ways to speed up the convergence of the ALS algorithm. This thesis discusses the use of Canonical Polyadic decomposition techniques and machine learning models in various data-driven domains, such as COVID-19, higher-order images and videos (e.g. RGB images and surveillance videos), and wildland fire datasets. The analysis begins with the application of CP decomposition and tensor completion framework to predict future COVID-19 infections using lower rank approximation of tensor. To solve the $l_1$ regularized problem, we use the Flexible Hybrid method based on Golub-Kahan process and the iterative soft thresholding algorithm standing on the proximal algorithm framework. We introduce the sampling method of alternating least square (SMALS) for computing Canonical Polyadic (CP) decomposition, which significantly reduces the computational cost of traditional CP decomposition. SMALS algorithm successfully estimates the COVID-19 infections up to the next week and quarter. Subsequently, we introduce an enhanced and optimized iteration of the Levenberg-Marquardt (LM) algorithm, specifically tailored for CP decomposition, with an emphasis on applications in image compression, reconstruction, and dimensionality reduction. We rigorously evaluate the performance of this algorithm across a diverse range of datasets, encompassing both randomly generated tensors and RGB images. Our proposed methodology demonstrates both efficiency and efficacy, delivering a significant reduction in computational cost in comparison to the conventional LM technique. Additionally, we explored the use of thermocouple temperature measurements to estimate turbulent kinetic energy (TKE) from wind speeds during a controlled burn in New Jersey, USA. Using machine learning models such as Deep Neural Networks and Random Forest Regressors, we aimed to predict TKE with thermocouple data despite weak direct correlations. By analyzing the data and visualizing the correlations, we achieved significant success in accurately estimating TKE, particularly through regression models. This achievement underscores the potential of machine learning to enhance fire behavior modeling and improve fire management strategies by providing more accurate predictive tools.

ProQuest ID

https://proquest.com/docview/3101847973