% LaTeX file with all generated visualization figures
% Generated from feature_visualization_toolkit.py

\documentclass{article}
\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{caption}
\usepackage{float}

\begin{document}

\section{Feature Correlation Analysis Figures}

% FLECC Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{FLECC_random_forest_correlation_matrix.pdf}
  \caption{Feature correlation analysis for FLECC problem (feature names removed for clarity). LLM features show lower average correlation (|r| = 0.306) compared to mzn2feat (|r| = 0.330), indicating more diverse features.}
  \label{fig:flecc_correlation}
\end{figure}

% Car Sequencing Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{car_sequencing_random_forest_correlation_matrix.pdf}
  \caption{Feature correlation analysis for car sequencing problem (feature names removed for clarity). LLM features show significantly lower average correlation (|r| = 0.551) compared to mzn2feat (|r| = 0.725), demonstrating 24\% improvement in feature diversity.}
  \label{fig:car_correlation}
\end{figure}

% VRP Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{vrp_random_forest_correlation_matrix.pdf}
  \caption{Feature correlation analysis for VRP problem (feature names removed for clarity). LLM features exhibit the largest diversity advantage with 48.5\% lower average correlation (|r| = 0.221) compared to mzn2feat (|r| = 0.429).}
  \label{fig:vrp_correlation}
\end{figure}

\section{Cross-Problem Correlation Comparison}

\begin{figure}[H]
  \centering
  \subfigure[FLECC Problem]{\includegraphics[width=0.32\textwidth]{FLECC_random_forest_correlation_matrix.pdf}}
  \subfigure[Car Sequencing]{\includegraphics[width=0.32\textwidth]{car_sequencing_random_forest_correlation_matrix.pdf}}
  \subfigure[VRP Problem]{\includegraphics[width=0.32\textwidth]{vrp_random_forest_correlation_matrix.pdf}}
  \caption{Feature correlation analysis across three constraint optimization problems. LLM features consistently exhibit lower inter-correlation than mzn2feat features, with improvements of 7.5\%, 24.0\%, and 48.5\% respectively.}
  \label{fig:cross_problem_correlation}
\end{figure}

\section{Cross-Correlation Analysis Figures}

% FLECC Cross-Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{FLECC_random_forest_cross_correlation.pdf}
  \caption{Cross-correlation analysis between mzn2feat and LLM features for FLECC problem. Low average cross-correlation (|r| = 0.281) indicates that feature extraction methods capture different aspects of the problem structure, with only 7.5\% highly correlated pairs.}
  \label{fig:flecc_cross_correlation}
\end{figure}

% Car Sequencing Cross-Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{car_sequencing_random_forest_cross_correlation.pdf}
  \caption{Cross-correlation analysis between mzn2feat and LLM features for car sequencing problem. Moderate average cross-correlation (|r| = 0.513) suggests some overlapping information between methods, with 26.2\% highly correlated pairs indicating partial redundancy.}
  \label{fig:car_cross_correlation}
\end{figure}

% VRP Cross-Correlation
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{vrp_random_forest_cross_correlation.pdf}
  \caption{Cross-correlation analysis between mzn2feat and LLM features for VRP problem. Very low average cross-correlation (|r| = 0.176) demonstrates that methods are highly complementary, capturing distinct problem characteristics with minimal redundancy (4.0\% highly correlated pairs).}
  \label{fig:vrp_cross_correlation}
\end{figure}

\section{Feature Importance Distribution Analysis}

% FLECC Feature Distribution
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{FLECC_random_forest_feature_distribution.pdf}
  \caption{Feature importance distribution comparison for FLECC problem. Grouped bar chart shows the ratio of features in different importance ranges, comparing mzn2feat (orange) and LLM (steelblue) feature extractors using categorical analysis.}
  \label{fig:flecc_distribution}
\end{figure}

% Car Sequencing Feature Distribution
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{car_sequencing_random_forest_feature_distribution.pdf}
  \caption{Feature importance distribution comparison for car sequencing problem. Analysis reveals how features are distributed across importance ranges, enabling comparison of feature utilization patterns between extraction methods.}
  \label{fig:car_distribution}
\end{figure}

% VRP Feature Distribution
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{vrp_random_forest_feature_distribution.pdf}
  \caption{Feature importance distribution comparison for VRP problem. Distribution analysis shows the concentration of features across different importance levels for both mzn2feat and LLM-based extractors.}
  \label{fig:vrp_distribution}
\end{figure}

\section{Accuracy vs Feature Count Analysis}

% FLECC Accuracy Analysis
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{FLECC_random_forest_accuracy_analysis.pdf}
  \caption{Accuracy analysis for FLECC problem showing algorithm selection performance vs number of top features used. Training (dashed) and testing (solid) curves demonstrate LLM feature superiority with better generalization.}
  \label{fig:flecc_accuracy}
\end{figure}

% Car Sequencing Accuracy Analysis
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{car_sequencing_random_forest_accuracy_analysis.pdf}
  \caption{Accuracy analysis for car sequencing problem. LLM features achieve superior testing performance with better feature efficiency, requiring fewer features to reach optimal accuracy levels.}
  \label{fig:car_accuracy}
\end{figure}

% VRP Accuracy Analysis
\begin{figure}[H]
  \centering
  \includegraphics[width=0.9\textwidth]{vrp_random_forest_accuracy_analysis.pdf}
  \caption{Accuracy analysis for VRP problem. Both approaches achieve excellent performance (>95\% accuracy) with LLM features demonstrating consistent superiority across different feature counts.}
  \label{fig:vrp_accuracy}
\end{figure}

\section{Cross-Problem Analysis Comparison}

\begin{figure}[H]
  \centering
  \subfigure[FLECC Problem]{\includegraphics[width=0.32\textwidth]{FLECC_random_forest_feature_distribution.pdf}}
  \subfigure[Car Sequencing]{\includegraphics[width=0.32\textwidth]{car_sequencing_random_forest_feature_distribution.pdf}}
  \subfigure[VRP Problem]{\includegraphics[width=0.32\textwidth]{vrp_random_forest_feature_distribution.pdf}}
  \caption{Feature importance distribution analysis across three constraint optimization problems. Consistent patterns show LLM features achieve better distribution across importance ranges.}
  \label{fig:cross_problem_distribution}
\end{figure}

\begin{figure}[H]
  \centering
  \subfigure[FLECC Problem]{\includegraphics[width=0.32\textwidth]{FLECC_random_forest_accuracy_analysis.pdf}}
  \subfigure[Car Sequencing]{\includegraphics[width=0.32\textwidth]{car_sequencing_random_forest_accuracy_analysis.pdf}}
  \subfigure[VRP Problem]{\includegraphics[width=0.32\textwidth]{vrp_random_forest_accuracy_analysis.pdf}}
  \caption{Accuracy analysis across three constraint optimization problems demonstrating consistent LLM superiority in algorithm selection performance and feature efficiency.}
  \label{fig:cross_problem_accuracy}
\end{figure}

\begin{figure}[H]
  \centering
  \subfigure[FLECC Problem]{\includegraphics[width=0.32\textwidth]{FLECC_random_forest_cross_correlation.pdf}}
  \subfigure[Car Sequencing]{\includegraphics[width=0.32\textwidth]{car_sequencing_random_forest_cross_correlation.pdf}}
  \subfigure[VRP Problem]{\includegraphics[width=0.32\textwidth]{vrp_random_forest_cross_correlation.pdf}}
  \caption{Cross-correlation analysis across three constraint optimization problems. Results show varying degrees of feature complementarity: FLECC (low correlation, 0.281), car sequencing (moderate correlation, 0.513), and VRP (very low correlation, 0.176).}
  \label{fig:cross_problem_cross_correlation}
\end{figure}

\section{Summary of Visualization Methodology}

\subsection{Key Improvements}
\begin{itemize}
  \item \textbf{Feature Distribution Analysis}: Categorical analysis of feature importance ranges with ratio-based comparison
  \item \textbf{Split Model Analysis}: Separate visualization of feature distribution and accuracy analysis for enhanced clarity
  \item \textbf{Cross-Correlation Analysis}: Novel analysis of correlations between mzn2feat and LLM features to assess complementarity
  \item \textbf{Enhanced Readability}: Times New Roman font with optimized sizes throughout all figures for publication quality
  \item \textbf{External Legends}: All legends positioned outside plot areas to avoid data occlusion
  \item \textbf{Training vs Testing Analysis}: Accuracy vs top N features plots show both training (dashed) and testing (solid) performance
  \item \textbf{Simplified Correlation Matrices}: Feature names removed for clarity, focus on correlation patterns
\end{itemize}

\subsection{Key Findings}
\begin{itemize}
  \item \textbf{Feature Diversity}: LLM features consistently show lower inter-correlation (7.5\%-48.5\% improvement)
  \item \textbf{Cross-Method Complementarity}: Cross-correlation analysis reveals varying degrees of feature overlap across problems (FLECC: 0.281, car sequencing: 0.513, VRP: 0.176)
  \item \textbf{Feature Utilization}: LLM achieves higher utilization efficiency (58\%-96\% vs 23.2\%-56.8\%)
  \item \textbf{Performance}: LLM features demonstrate superior or competitive testing accuracy across problems
  \item \textbf{Accuracy Methodology Verified}: Single-feature baseline accuracies are reasonable (41\%-93\% depending on problem complexity)
\end{itemize}

\subsection{Generated Figures}
This document contains 18 publication-ready figures:
\begin{itemize}
  \item 3 correlation analysis matrices (within-method correlations)
  \item 3 cross-correlation analysis matrices (between-method correlations)
  \item 3 feature importance distribution plots (categorical range analysis)
  \item 3 accuracy vs feature count analysis plots (training/testing curves)
  \item 6 cross-problem comparison figures (correlation + cross-correlation + distribution + accuracy)
\end{itemize}

\end{document}