COMPUTATIONAL METHODS IN MACHINE LEARNING: TRANSPORT MODEL, HAAR WAVELET, DNA CLASSIFICATION, AND MRI

Abstract

With the increasing amount of raw data generation produced every day, it

has become pertinent to develop new techniques for data representation, analyses,

and interpretation. Motivated by real-world applications, there is a trending interest

in techniques such as dimensionality reduction, wavelet decomposition, and

classication methods that allow for better understanding of data. This thesis details

the development of a new non-linear dimension reduction technique based on

transport model by advection. We provide a series of computational experiments,

and practical applications in hyperspectral images to illustrate the strength of our

algorithm. In wavelet decomposition, we construct a novel Haar approximation

technique for functions f in the Lp-space, 0 < p < 1, such that the approximants

have support contained in the support of f. Furthermore, a classification algorithm

to study tissue-specific deoxyribonucleic acids (DNA) is constructed using the support

vector machine. In magnetic resonance imaging, we provide an extension of

the T2-store-T2 magnetic resonance relaxometry experiment used in the analysis

of magnetization signal from 2 to N exchanging sites, where N >= 2.