Type Ia supernovae (SNe Ia) play a vital role in the study of many topics of astrophysics. They act as cosmological probes through their well-established nature as precise standardizable candles. This nature can be described empirically by the systematic relationship between the width of their light-curve and their peak luminosity, otherwise known as the Phillips relation. As extragalactic distance indicators, SNe Ia aid in constraining the nature of dark energy. SNe Ia also enrich the universe with iron-group products, and provide insight into our understanding of stellar evolution as a whole. To fully and precisely take advantage of the standardizable properties of SNe Ia, their time evolution must be fully understood, including the nature of their origin. Unfortunately, the exact progenitor systems of SNe Ia are still uncertain and are a popular topic in the study of SNe Ia. The different theorized progenitor scenarios and explosion mechanisms that SNe Ia undergo stem from the diversity of their observable properties. Understanding the causes of the variation seen between SNe Ia is imperative in minimizing the Hubble residual, which is used to deduce cosmological parameters such as the Hubble constant. Due to the complexities of supernova physics, the variation observed in SNe Ia are often described using empirical models. Recent advances in statistical and machine-learning techniques have led to models that provide useful constraints on theories that link observables to the underlying progenitor system. Although the time-dependent nature of SNe Ia leads to difficulty in obtaining large samples in order to treat observations statistically, recent surveys of astronomical transients have led to sample sizes large enough such that modern machine-learning techniques can be applied. The goal of this thesis is to use this increase in data available to create empirical models that will aid in the classification and prediction of SN Ia properties, which will further constrain the progenitor problem. Specifically, these models will be created using a combination of both observed spectroscopy and photometry. In doing so, correlations between the two regimes are found which are useful for constraining spectroscopic models and improving light-curve models of SNe Ia. This thesis is organized in the following manner: Chapter 1 reviews the fundamental nature of SNe Ia along with previously theorized progenitor systems and explosion mechanisms; Chapter 2 discusses the observational diversity of SNe Ia, including some of the relevant subtypes of SNe Ia and the observational data used in empirical models created here; Chapter 3 details a cluster analysis of a sample of SNe Ia that leads to a robust model for classifying SNe Ia; Chapter 4 reviews ix the light-curve-fitter SNooPy and, using SNooPy, illustrates the limitations of the color-stretch parameter sBV in the near-infrared; Chapter 5 discusses a technique using principal component analysis to extrapolate NIR spectra of SNe Ia using optical spectroscopy; Chapter 6 proposes a method of modeling residuals from aforementioned extrapolations to more thoughtfully provide correlated uncertainties for the application of light-curve calculations; Chapter 7 studies the principal components from the extrapolation model in Chapter 5 in more detail, and relates them back to the classification scheme defined in Chapter 3; finally, Chapter 8 provides a summary of the most notable conclusions in this work.