[KB-273] Rewrite problem formulation to include the challenges

report_thesis/src/sections/problem_definition.tex

@@ -1,6 +1,6 @@
 \section{Problem Definition}\label{sec:problem_definition}
 The objective of this research is to predict major oxide compositions from \gls{libs} data.
-We aim to enhance the accuracy and robustness of these predictions by developing and validating a computational methodology that addresses the challenges of such quantification of elements in soil samples from \gls{libs} data. 
+We aim to enhance the accuracy and robustness of these predictions by developing and validating a computational methodology that addresses the challenges of such quantification of elements in soil samples from \gls{libs} data.
 This objective presents several significant challenges, including the high dimensionality of spectral data, multicollinearity, matrix effects, and limited data availability.
 
 A fundamental premise of this research posits that by effectively addressing these challenges, the accuracy and robustness of predicting elemental concentrations from \gls{libs} data can be significantly enhanced. This assumption is supported by several key studies in the field.
@@ -70,4 +70,5 @@ \subsubsection{Data Availability}
 Due to the high cost of data collection, datasets are often small. This limits the number of samples available for evaluation, affecting the generalizability and robustness of the models\cite{p9_paper}.
 
 \subsection{Problem Formulation}
-The objective of this research is to develop a computational model, denoted as $\mathcal{F}: \mathbb{R}^N \rightarrow \mathbb{R}^{n_o}$, to predict major oxide concentrations in geological samples from processed \gls{libs} spectral data. 
+The objective of this research is to develop a computational model, denoted as $\mathcal{F}: \mathbb{R}^N \rightarrow \mathbb{R}^{n_o}$, to predict major oxide concentrations in geological samples from processed \gls{libs} spectral data.
+This task is complicated by the high dimensionality of the data, multicollinearity among spectral features, matrix effects that alter emission intensities, and the limited availability of data.