\documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\geometry{margin=1in}
\usepackage{graphicx}
\usepackage{booktabs}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{longtable}
\usepackage{hyperref}
\usepackage{multirow}
\usepackage{graphicx}
\usepackage{booktabs}
\title{\textbf{Supplementary Material \\ XG-PUL: A Network-Based Framework for Disease Gene Prioritization Using Graph Representation Learning and Positive-Unlabeled Learning}}
\author{\textbf{Mahdiyeh Ayouman}$^{1}$, \textbf{Zahra Narimani}$^{1}$}
\date{\small $^{1}$Department of Computer Science, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran}

\begin{document}
	
	\maketitle
	\tableofcontents
	\newpage




\section{Section 1: Feature Engineering and Scenario Ablation Analysis}
	
	

\subsection{Ablation Study 1: Feature Space Hybridization}
A crucial phase in the development of the XG-PUL framework involved validating the selection of both the network embedding configuration and the final feature representation. To justify the embedding strategy, we first evaluated four Node2Vec hyperparameter configurations, including baseline, high-dimensional, deep-exploration, and ultra-high-dimensional settings. The corresponding hyperparameters, including embedding dimension, walk strategy ($p$ and $q$), walk length, and sampling density, are summarized in Table~\ref{tab:hyperparameters}.

The embedding configurations were assessed using an internal validation setting, in which held-out known disease genes (excluded from the seed set) were used for evaluation rather than a conventional train/test split. Representative results for seven complex diseases are presented in Table~\ref{tab:embedding_results}. Across these diseases, the HighDim configuration consistently achieved the strongest or near-best predictive performance in terms of both AUPR and F1@500. Based on these results, HighDim was selected as the default embedding configuration for all subsequent experiments.


After selecting the optimal embedding configuration, we evaluated three alternative feature representations:
\begin{itemize}
	\item \textbf{Embedding Only (Top-150):} Node2Vec embeddings only after supervised feature selection.
	\item \textbf{Embedding + Topological Features (Top-150):} Node2Vec embeddings integrated with graph-derived topological features followed by supervised feature selection.
	\item \textbf{Embedding + Topological Features (All):} The complete feature set without feature selection.
\end{itemize}

Representative comparisons for these seven scenarios are presented in Table~\ref{tab:final_scenario_comparison}. Across all evaluated diseases, integrating graph-derived topological features consistently improved predictive performance compared with using embeddings alone. Although retaining all features produced a slight performance gain for prostate cancer, the improvement was marginal relative to the increased computational cost. These results justify the adoption of the combined feature representation with the top 150 selected features in the final XG-PUL framework.

\begin{table}[htbp]
	\centering
	\caption{Performance comparison of different feature representations for disease gene prioritization across seven complex diseases.}
	\label{tab:final_scenario_comparison}
	\resizebox{\linewidth}{!}{%
		\begin{tabular}{llcc}
			\toprule
			\textbf{Disease} & \textbf{Scenario} & \textbf{AUPR} & \textbf{F1@500} \\
			\midrule
			
			\multirow{3}{*}{Schizophrenia}
			& Embed\_only\_top150 & 0.1767 & 0.1445 \\
			& Embed+Topological\_Features\_top150 & 0.1712 & 0.2069 \\
			& Embed+Topological\_Features\_all & 0.1836 & 0.2241\\
			\midrule
			
			\multirow{3}{*}{Liver Cirrhosis}
			& Embed\_only\_top150 & 0.0399 & 0.1086 \\
			& Embed+Topological\_Features\_top150 & 0.0320 & 0.0848 \\
			& Embed+Topological\_Features\_all & 0.0410 & 0.0848\\
			\midrule
				

				
			\multirow{3}{*}{Colorectal Carcinoma}
			& Embed\_only\_top150 & 0.2948 & 0.1828\\
			& Embed+Topological\_Features\_top150 & 0.3063 & 0.1841 \\
			& Embed+Topological\_Features\_all & 0.3139 & 0.1867\\
			\midrule
			

			
			\multirow{3}{*}{Intellectual Disability}
			& Embed\_only\_top150 & 0.1194 & 0.1671\\
			& Embed+Topological\_Features\_top150 & 0.3063 & 0.1841 \\
			& Embed+Topological\_Features\_all & 0.1142 & 0.1718\\
			\midrule
			

			
			\multirow{3}{*}{Drug-Induced Liver Disease}
			& Embed\_only\_top150 & 0.0151 & 0.0572\\
			& Embed+Topological\_Features\_top150 & 0.0168 & 0.0604 \\
			& Embed+Topological\_Features\_all & 0.0186 & 0.0731\\
			\midrule
			

			
			\multirow{3}{*}{Depressive Disorder}
			& Embed\_only\_top150 & 0.0950 & 0.1751\\
			& Embed+Topological\_Features\_top150 & 0.1007 & 0.1696 \\
			& Embed+Topological\_Features\_all & 0.1116 & 0.1895\\
			\midrule

			
			\multirow{3}{*}{Chronic Alcoholic Intoxication}
			& Embed\_only\_top150 & 0.0135 & 0.0692\\
			& Embed+Topological\_Features\_top150 & 0.0142 & 0.0692 \\
			& Embed+Topological\_Features\_all & 0.0151 & 0.0589\\
			

			
			\bottomrule
		\end{tabular}%
	}
\end{table}



\begin{table}[ht]
	\centering
	\caption{Hyperparameter settings for Node2Vec embedding configurations used in the study.}
	\label{tab:hyperparameters}
	\begin{tabular}{lcccccccc}
		\toprule
		\textbf{Configuration} & \textbf{Dim.} & \textbf{Walk Len.} & \textbf{Num. Walks} & \textbf{Window} & \textbf{Min. Count} & \textbf{p} & \textbf{q} \\ 
		\midrule
		Baseline       & 128 & 80 & 10 & 10 & 3 & 1.0 & 1.0 \\
		High-Dim       & 256 & 80 & 10 & 10 & 3 & 1.0 & 1.0 \\
		Deep-Explore   & 128 & 80 & 20 & 10 & 3 & 0.5 & 2.0 \\
		Ultra-High-Dim & 500 & 80 & 20 & 10 & 3 & 1.0 & 1.0 \\ 
		\bottomrule
	\end{tabular}
\end{table}
	




\begin{table}[htbp]
	\centering
	\caption{Performance comparison of node2vec embedding configurations across seven complex diseases.}
	\label{tab:embedding_results}
	\begin{tabular}{@{}llcc@{}}
		\toprule
		\textbf{Disease} & \textbf{Embedding} & \textbf{AUPR} & \textbf{F1@500} \\
		\midrule
		\textbf{Chronic Alcoholic Intoxication} & Baseline & 0.0154 & 0.0769 \\
		& DeepExplore & 0.0207 & 0.0846 \\
		& HighDim & 0.0136 & 0.0538 \\
		& UltraHighDim & 0.0152 & 0.0615 \\
		\midrule
		\textbf{Colorectal Carcinoma} & Baseline & 0.2383 & 0.1732 \\
		& DeepExplore & 0.2539 & 0.1640 \\
		& HighDim & 0.2956 & 0.1820 \\
		& UltraHighDim & 0.2608 & 0.1697 \\
		\midrule
		\textbf{Depressive Disorder} & Baseline & 0.0534 & 0.1208 \\
		& DeepExplore & 0.0824 & 0.1519 \\
		& HighDim & 0.0965 & 0.1652 \\
		& UltraHighDim & 0.0816 & 0.1475 \\
		\midrule
		\textbf{Liver Cirrhosis} & Baseline & 0.0132 & 0.0543 \\
		& DeepExplore & 0.0333 & 0.0849 \\
		& HighDim & 0.0389 & 0.0985 \\
		& UltraHighDim & 0.0262 & 0.0713 \\
		\midrule
		\textbf{Schizophrenia} & Baseline & 0.1241 & 0.1780 \\
		& DeepExplore & 0.1552 & 0.2015 \\
		& HighDim & 0.1697 & 0.2042 \\
		& UltraHighDim & 0.1541 & 0.1952 \\
		\midrule
		\textbf{Drug-Induced Liver Disease} & Baseline & 0.0068 & 0.0413 \\
		& DeepExplore & 0.0126 & 0.0509 \\
		& HighDim & 0.0125 & 0.0541 \\
		& UltraHighDim & 0.0203 & 0.0890 \\
		\midrule
		\textbf{Intellectual Disability} & Baseline & 0.0807 & 0.1443 \\
		& DeepExplore & 0.1028 & 0.1519 \\
		& HighDim & 0.1180 & 0.1652 \\
		& UltraHighDim & 0.1112 & 0.1652 \\
		\bottomrule
	\end{tabular}
\end{table}

\subsection{Ablation Study 2: Dimensionality Optimization and Computational Efficiency}


After confirming the benefit of integrating Node2Vec embeddings with graph-derived topological features, we next investigated the optimal feature dimensionality. Including all available topological descriptors introduces substantial redundancy and increases computational complexity, particularly for ensemble-based positive–unlabeled learning.

Our evaluation demonstrated that the feature representation consisting of the top 150 selected features achieved performance comparable to the complete feature set across all representative diseases. Although the complete feature set yielded a slight improvement for prostate cancer, this gain was marginal relative to the increased computational cost. Consequently, selecting the top 150 features provides a better balance between predictive performance and computational efficiency and was therefore adopted throughout the proposed framework.

\section{Section 2: Comprehensive Performance Evaluation Tables}

\subsection{Evaluation Metrics and Methodological Summary}
To provide a rigorous numerical foundation for the evaluation curves presented in the subsequent sections, this section summarizes the empirical performance metrics across the investigated complex diseases. To prevent repetitive and oversized tabular layouts across all independent $K$ thresholds, we report the macro-averaged performance metrics (Mean $\pm$ Standard Deviation) calculated across the entire progressive threshold spectrum, spanning $K \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$.

The proposed \texttt{XG-PUL} framework is benchmarked against classical network propagation algorithms (\texttt{DIAMOnD} and \texttt{RWR}), community-detection baselines (\texttt{MCL}), and explainable graph neural network variations (\texttt{XGDAG - GNNExplainer} and \texttt{XGDAG - GraphSVX}). The evaluation tracks three standard metrics: Precision, Recall, and $F_1$-score.

\subsection{Aggregated Performance Profiles Across Disease Modules}

% --- Table S1: Breast Cancer ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Malignant Neoplasm of Breast (C0006142)}}
	\label{tab:table_s1}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.908 $\pm$ 0.110} & \textbf{0.168 $\pm$ 0.151} & \textbf{0.248 $\pm$ 0.198} \\
		\texttt{XGDAG - GraphSVX} & 0.626 $\pm$ 0.108 & 0.111 $\pm$ 0.101 & 0.164 $\pm$ 0.131 \\
		\texttt{XGDAG - GNNExplainer} & 0.625 $\pm$ 0.108 & 0.111 $\pm$ 0.100 & 0.164 $\pm$ 0.130 \\
		\texttt{DIAMOnD} & 0.621 $\pm$ 0.130 & 0.109 $\pm$ 0.102 & 0.161 $\pm$ 0.132 \\
		\texttt{RWR} & 0.510 $\pm$ 0.099 & 0.095 $\pm$ 0.089 & 0.139 $\pm$ 0.116 \\
		\texttt{MCL} & 0.434 $\pm$ 0.037 & 0.085 $\pm$ 0.079 & 0.125 $\pm$ 0.103 \\
		\bottomrule
	\end{tabular}
\end{table}



% --- Table S2: Schizophrenia ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Schizophrenia (0036341)}.}
	\label{tab:table_s2}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.493 $\pm$ 0.236} & \textbf{0.190 $\pm$ 0.146} & \textbf{0.204 $\pm$ 0.112} \\
		\texttt{XGDAG - GraphSVX} & 0.220 $\pm$ 0.058 & 0.106 $\pm$ 0.092 & 0.110 $\pm$ 0.070 \\
		\texttt{XGDAG - GNNExplainer} & 0.220 $\pm$ 0.058 & 0.107 $\pm$ 0.092 & 0.110 $\pm$ 0.070 \\
		\texttt{DIAMOnD} & 0.213 $\pm$ 0.083 & 0.091 $\pm$ 0.074 & 0.095 $\pm$ 0.056 \\
		\texttt{RWR} & 0.148 $\pm$ 0.027 & 0.084 $\pm$ 0.081 & 0.083 $\pm$ 0.062 \\
		\texttt{MCL} & 0.119 $\pm$ 0.109 & 0.023 $\pm$ 0.010 & 0.029 $\pm$ 0.011 \\
		\bottomrule
	\end{tabular}
\end{table}


% --- Table S3: Liver Cirrhosis ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Liver Cirrhosis (C0023893)}.}
	\label{tab:table_s3}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.080 $\pm$ 0.081} & \textbf{0.361 $\pm$ 0.217} & \textbf{0.082 $\pm$ 0.032} \\
		\texttt{XGDAG - GraphSVX} & 0.020 $\pm$ 0.010 & 0.164 $\pm$ 0.132 & 0.026 $\pm$ 0.007 \\
		\texttt{XGDAG - GNNExplainer} & 0.020 $\pm$ 0.010 & 0.157 $\pm$ 0.131 & 0.025 $\pm$ 0.005 \\
		\texttt{DIAMOnD} & 0.001 $\pm$ 0.001 & 0.012 $\pm$ 0.012 & 0.001 $\pm$ 0.002 \\
		\texttt{RWR} & 0.014 $\pm$ 0.007 & 0.137 $\pm$ 0.112 & 0.021 $\pm$ 0.009 \\
		\texttt{MCL} & 0.008 $\pm$ 0.008 & 0.062 $\pm$ 0.044 & 0.011 $\pm$ 0.009 \\
		\bottomrule
	\end{tabular}
\end{table}


% --- Table S4: Colorectal Carcinoma ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Colorectal Carcinoma (C0009402)}.}
	\label{tab:table_s4}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.799 $\pm$ 0.164} & \textbf{0.170 $\pm$ 0.147} & \textbf{0.239 $\pm$ 0.178} \\
		\texttt{XGDAG - GraphSVX} & 0.551 $\pm$ 0.112 & 0.118 $\pm$ 0.105 & 0.165 $\pm$ 0.125 \\
		\texttt{XGDAG - GNNExplainer} & 0.552 $\pm$ 0.112 & 0.118 $\pm$ 0.105 & 0.165 $\pm$ 0.125 \\
		\texttt{DIAMOnD} & 0.535 $\pm$ 0.168 & 0.104 $\pm$ 0.087 & 0.147 $\pm$ 0.103 \\
		\texttt{RWR} & 0.411 $\pm$ 0.039 & 0.100 $\pm$ 0.094 & 0.138 $\pm$ 0.113 \\
		\texttt{MCL} & 0.358 $\pm$ 0.039 & 0.086 $\pm$ 0.079 & 0.120 $\pm$ 0.095 \\
		\bottomrule
	\end{tabular}
\end{table}


% --- Table S5: Prostate Cancer ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Malignant Neoplasm of Prostate (C0376358)}.}
	\label{tab:table_s5}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.780 $\pm$ 0.194} & \textbf{0.191 $\pm$ 0.160} & \textbf{0.255 $\pm$ 0.179} \\
		\texttt{XGDAG - GraphSVX} & 0.523 $\pm$ 0.134 & 0.129 $\pm$ 0.111 & 0.172 $\pm$ 0.123 \\
		\texttt{XGDAG - GNNExplainer} & 0.519 $\pm$ 0.128 & 0.129 $\pm$ 0.111 & 0.171 $\pm$ 0.123 \\
		\texttt{DIAMOnD} & 0.537 $\pm$ 0.286 & 0.106 $\pm$ 0.089 & 0.141 $\pm$ 0.094 \\
		\texttt{RWR} & 0.376 $\pm$ 0.085 & 0.103 $\pm$ 0.096 & 0.135 $\pm$ 0.107 \\
		\texttt{MCL} & 0.253 $\pm$ 0.147 & 0.041 $\pm$ 0.024 & 0.058 $\pm$ 0.031 \\
		\bottomrule
	\end{tabular}
\end{table}

% --- Table S6: Intellectual Disability ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Intellectual Disability (C3714756)}.}
	\label{tab:table_s6}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.380 $\pm$ 0.160} & \textbf{0.168 $\pm$ 0.135} & \textbf{0.172 $\pm$ 0.099} \\
		\texttt{XGDAG - GraphSVX} & 0.204 $\pm$ 0.082 & 0.101 $\pm$ 0.090 & 0.100 $\pm$ 0.065 \\
		\texttt{XGDAG - GNNExplainer} & 0.205 $\pm$ 0.083 & 0.100 $\pm$ 0.089 & 0.100 $\pm$ 0.065 \\
		\texttt{DIAMOnD} & 0.185 $\pm$ 0.089 & 0.080 $\pm$ 0.065 & 0.082 $\pm$ 0.048 \\
		\texttt{RWR} & 0.147 $\pm$ 0.028 & 0.087 $\pm$ 0.081 & 0.085 $\pm$ 0.061 \\
		\texttt{MCL} & 0.138 $\pm$ 0.018 & 0.084 $\pm$ 0.077 & 0.083 $\pm$ 0.058 \\
		\bottomrule
	\end{tabular}
\end{table}


% --- Table S7: Bipolar Disorder ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Bipolar Disorder (C0005586)}.}
	\label{tab:table_s7}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.158 $\pm$ 0.079} & \textbf{0.174 $\pm$ 0.132} & \textbf{0.111 $\pm$ 0.052} \\
		\texttt{XGDAG - GraphSVX} & 0.086 $\pm$ 0.051 & 0.093 $\pm$ 0.080 & 0.057 $\pm$ 0.023 \\
		\texttt{XGDAG - GNNExplainer} & 0.086 $\pm$ 0.051 & 0.093 $\pm$ 0.080 & 0.057 $\pm$ 0.023 \\
		\texttt{DIAMOnD} & 0.065 $\pm$ 0.045 & 0.052 $\pm$ 0.029 & 0.038 $\pm$ 0.016 \\
		\texttt{RWR} & 0.053 $\pm$ 0.012 & 0.081 $\pm$ 0.073 & 0.047 $\pm$ 0.026 \\
		\texttt{MCL} & 0.043 $\pm$ 0.045 & 0.019 $\pm$ 0.007 & 0.017 $\pm$ 0.009 \\
		\bottomrule
	\end{tabular}
\end{table}

% --- Table S8: Drug-Induced Liver Disease ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Drug-Induced Liver Disease (C0860207)}.}
	\label{tab:table_s8}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.032 $\pm$ 0.007} & \textbf{0.229 $\pm$ 0.197} & \textbf{0.044 $\pm$ 0.018} \\
		\texttt{XGDAG - GraphSVX} & 0.034 $\pm$ 0.032 & 0.137 $\pm$ 0.107 & 0.033 $\pm$ 0.005 \\
		\texttt{XGDAG - GNNExplainer} & 0.033 $\pm$ 0.032 & 0.137 $\pm$ 0.109 & 0.032 $\pm$ 0.005 \\
		\texttt{DIAMOnD} & 0.004 $\pm$ 0.005 & 0.027 $\pm$ 0.018 & 0.007 $\pm$ 0.006 \\
		\texttt{RWR} & 0.008 $\pm$ 0.006 & 0.085 $\pm$ 0.079 & 0.014 $\pm$ 0.010 \\
		\texttt{MCL} & 0.007 $\pm$ 0.005 & 0.057 $\pm$ 0.043 & 0.012 $\pm$ 0.009 \\
		\bottomrule
	\end{tabular}
\end{table}


% --- Table S9: Depressive Disorder ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Depressive Disorder (C0011581)}.}
	\label{tab:table_s9}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.334 $\pm$ 0.177} & \textbf{0.171 $\pm$ 0.137} & \textbf{0.159 $\pm$ 0.086} \\
		\texttt{XGDAG - GraphSVX} & 0.216 $\pm$ 0.098 & 0.119 $\pm$ 0.098 & 0.109 $\pm$ 0.062 \\
		\texttt{XGDAG - GNNExplainer} & 0.220 $\pm$ 0.106 & 0.119 $\pm$ 0.098 & 0.109 $\pm$ 0.062 \\
		\texttt{DIAMOnD} & 0.185 $\pm$ 0.110 & 0.080 $\pm$ 0.054 & 0.079 $\pm$ 0.037 \\
		\texttt{RWR} & 0.126 $\pm$ 0.029 & 0.091 $\pm$ 0.084 & 0.080 $\pm$ 0.056 \\
		\texttt{MCL} & 0.059 $\pm$ 0.035 & 0.025 $\pm$ 0.015 & 0.026 $\pm$ 0.015 \\
		\bottomrule
	\end{tabular}
\end{table}

% --- Table S10: Chronic Alcoholic Intoxication ---
\begin{table}[htbp]
	\caption{Macro-averaged performance evaluation across the complete $K$ threshold spectrum ($K  \in [25, 50, 100, 200, 500, 750,$ $1000, 1500, 2000, 2500, 3000]$) for \textbf{Chronic Alcoholic Intoxication (C0001973)}.}
	\label{tab:table_s10}
	\centering
	\small
	\begin{tabular}{lccc}
		\toprule
		\textbf{Method} & \textbf{Mean Precision} & \textbf{Mean Recall} & \textbf{Mean $F_1$-score} \\
		\midrule
		\texttt{\textbf{XG-PUL}} & \textbf{0.061 $\pm$ 0.050} & \textbf{0.140 $\pm$ 0.117} & \textbf{0.052 $\pm$ 0.017} \\
		\texttt{XGDAG - GraphSVX} & 0.042 $\pm$ 0.025 & 0.092 $\pm$ 0.073 & 0.036 $\pm$ 0.009 \\
		\texttt{XGDAG - GNNExplainer} & 0.042 $\pm$ 0.025 & 0.093 $\pm$ 0.074 & 0.037 $\pm$ 0.010 \\
		\texttt{DIAMOnD} & 0.022 $\pm$ 0.021 & 0.046 $\pm$ 0.026 & 0.023 $\pm$ 0.015 \\
		\texttt{RWR} & 0.041 $\pm$ 0.030 & 0.091 $\pm$ 0.080 & 0.034 $\pm$ 0.008 \\
		\texttt{MCL} & 0.012 $\pm$ 0.011 & 0.018 $\pm$ 0.010 & 0.009 $\pm$ 0.004 \\
		\bottomrule
	\end{tabular}
\end{table}
\newpage


	\newpage
	\section{Section 3: Top-$K$ Threshold Comparative Analysis}
	
	\subsection{Methodological Context and Robustness Evaluation}
	To thoroughly investigate the stability and predictive robustness of the proposed \texttt{XG-PUL} framework, we analyze its performance against baseline and state-of-the-art models (including \texttt{DIAMOnD}, \texttt{RWR}, \texttt{MCL}, and \texttt{XGDAG}-based variations) across ten progressive top-$K$ selection cutoffs ranging from $K=25$ to $K=3000$. 
	
	To ensure maximum visual clarity and preserve the original high-resolution rendering of the evaluation metrics across all disease benchmarks, each threshold configuration is presented independently in a full-width sequential layout below.
	
	As demonstrated in the following sequential plots, \texttt{XG-PUL} consistently maintains an edge or matches the most competitive configurations under tight thresholds (e.g., $K=25, 50, 100$), which are crucial for immediate wet-lab experimental validation. Furthermore, as the threshold expands to wider bounds ($K \ge 500$), our model yields highly robust recall and stable $F_1$-score trajectories, confirming that integrating graph representation learning with Positive-Unlabeled learning successfully circumvents the negative label noise inherent in classical network propagation techniques.
	
	\newpage
	\subsection{Sequential Threshold Performance Plots}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K25.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 25$.}
		\label{fig:k25}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K50.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 50$.}
		\label{fig:k50}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K100.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 100$.}
		\label{fig:k100}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K200.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 200$.}
		\label{fig:k200}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K500.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 500$.}
		\label{fig:k500}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K750.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 750$.}
		\label{fig:k750}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K1000.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 1000$.}
		\label{fig:k1000}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K1500.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 1500$.}
		\label{fig:k1500}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K2000.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 2000$.}
		\label{fig:k2000}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K2500.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 2500$.}
		\label{fig:k2500}
	\end{figure}
	
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{BarChart_K3000.png}
		\caption{Comparative evaluation metrics across all ten complex diseases for top-$K$ threshold $K = 3000$.}
		\label{fig:k3000}
	\end{figure}
	
	\newpage
	\section{Section 4: Continuous $F_1$-Score Trajectory Analysis across Top-$K$ Thresholds}
	
	\subsection{Methodological Context and Cross-Disease Trends}
	While the bar charts in Section S2 isolate individual evaluation thresholds, analyzing the continuous trajectory of the $F_1$-score across a dense grid of $K$ values provides deeper insights into model stability. In disease gene prioritization, a frequent challenge for network propagation algorithms (such as \texttt{RWR} and \texttt{DIAMOnD}) is the rapid decay of precision or early saturation of recall, which causes a sharp drop in the $F_1$-score as the candidate list expands.
	
	To demonstrate how the integration of embedding selections with bagging-based Positive-Unlabeled learning mitigates this limitation, we plot the $F_1$-score as a continuous function of $K$ (from $K=25$ up to $K=2500$). 
	
	Following the aggregate overview, Figures~\ref{fig:f1_breast} through \ref{fig:f1_alcoholic} disclose the independent, high-resolution $F_1$-score comparison curves for each distinct disease in our benchmark dataset. These plots verify that the predictive superiority of \texttt{XG-PUL} is sustained across varying disease modules and topological contexts, rather than being skewed by a single highly-characterized disease.
	

	
%	\newpage
	\subsection{Disease-Specific $F_1$-Score Comparison Curves}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Malignant_neoplasm_of_breast.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Malignant Neoplasm of Breast.}
		\label{fig:f1_breast}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Schizophrenia.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Schizophrenia.}
		\label{fig:f1_schizophrenia}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Liver_Cirrhosis.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Liver Cirrhosis.}
		\label{fig:f1_liver_cirrhosis}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Colorectal_Carcinoma.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Colorectal Carcinoma.}
		\label{fig:f1_colorectal}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Malignant_neoplasm_of_prostate.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Malignant Neoplasm of Prostate.}
		\label{fig:f1_prostate}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Bipolar_Disorder.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Bipolar Disorder.}
		\label{fig:f1_bipolar}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Drug-Induced_Liver_Disease.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Drug-Induced Liver Disease.}
		\label{fig:f1_drug_liver}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Depressive_disorder.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Depressive Disorder.}
		\label{fig:f1_depression}
	\end{figure}
	
	\begin{figure}[htbp]
		\centering
		\includegraphics[width=0.95\textwidth]{F1_Comparison_Chronic_Alcoholic_Intoxication.png}
		\caption{Continuous $F_1$-score trajectory comparison across varying top-$K$ thresholds for Chronic Alcoholic Intoxication.}
		\label{fig:f1_alcoholic}
	\end{figure}
	
	

\newpage
\section{Section 5: Enrichment Analysis}


Table 11 summarizes the enrichment analysis results for the ten diseases investigated in this study. For each disease, the most statistically significant pathway, ontology, or related disease—as identified by our proposed \texttt{XG-PUL} framework is reported. Model-prioritized genes were systematically cross-referenced with curated gene set databases using the Enrichr platform, including DisGeNET, GO Biological Process (2026), KEGG (2026), Reactome Pathways (2024), and WikiPathways (2024 Human). These cross-referenced results, aggregated in the corresponding tables (\texttt{DisGeNET\_table}, \texttt{GO\_Biological\_Process\_2026\_table}, \texttt{KEGG\_2026\_table}, \texttt{Reactome\_Pathways\_2024\_table}, and \texttt{WikiPathways\_2024\_Human\_table}), highlight the most relevant pathophysiological modules underlying each phenotype. This comprehensive approach provides an objective biological validation of the candidate targets predicted by our approach.


\begin{longtable}{p{3.8cm} p{3.2cm} p{6.8cm} p{2.2cm}}
	\caption{Enrichment analysis for the considered diseases. We report the most enriched GO, pathway, or disease.} \label{tab:enrichment_analysis} \\
	\toprule
	\textbf{Disease} & \textbf{Enriched Pathway / GO / Disease} & \textbf{Details} & \textbf{Reference} \\
	\midrule
	\endhead
	
	\bottomrule
	\endfoot 
	
	Malignant neoplasm of breast (C0006142) & SUMOylation of SUMOylation Proteins (Reactome) & The top predicted genes are most highly enriched for "SUMOylation of SUMOylation Proteins", highlighting the prominent role of SUMO modification processes in the pathogenesis of breast cancer. SUMOylation regulates DNA repair, transcription, and protein stability, all of which are critically implicated in tumor development. & Seeler \& Dejean, 2017; Hendriks \& Vertegaal, 2016 \\
	\hline
	Schizophrenia (C0036341) & Nervous System Development (Reactome) & The prioritized genes showed significant enrichment for \textit{Nervous System Development}, a term that is highly relevant to schizophrenia and consistent with the established neurodevelopmental contribution to its pathophysiology, even though signal transduction- and GPCR-related pathways ranked higher by statistical significance. & Owen et al., 2016; Kahn et al., 2015 \\
	\hline
	Liver cirrhosis (C0023893) & Integrin Cell Surface Interactions (Reactome) & Genes prioritized by the model showed highest enrichment for "Integrin Cell Surface Interactions". This emphasizes the central role of integrin-mediated signaling and extracellular matrix (ECM) reorganization in liver fibrogenesis and the pathogenesis of cirrhosis, as consistently reported in recent research. & Bataller \& Brenner, 2005; Kisseleva \& Brenner, 2008 \\
	\hline
	Colorectal carcinoma (C0009402) & Regulation of TP53 Activity (Reactome) & Genes prioritized by the model show the highest enrichment in “Regulation of TP53 Activity,” reflecting TP53’s pivotal role in cell cycle regulation, DNA repair, and apoptosis in colorectal cancer pathogenesis. Dysfunction in this pathway is a hallmark of tumorigenesis. & Fearon \& Vogelstein, 1990; Liebl \& Hofmann, 2021 \\
	\hline
	Malignant neoplasm of prostate (C0376358) & Immune System (Reactome) & The top enrichment in \textit{Immune System} pathways is consistent with the known contribution of immune and inflammatory processes to prostate cancer development and progression, supporting current insights into tumor immunobiology. & Drake et al., 2014; Sfanos \& De Marzo, 2012 \\
	\hline
	Intellectual disability (C3714756) & Gene Expression (Transcription) (Reactome) & The top enrichment in gene expression/transcription-related pathways is consistent with the established role of transcriptional and epigenetic dysregulation in the etiology of intellectual disability, supporting evidence that chromatin modification and gene regulation defects contribute to neurodevelopmental disorders. & Mossink et al., 2021; Ciptasari \& van Bokhoven, 2020 \\
	\hline
	Bipolar disorder (C0005586) & Neuronal System (Reactome) & Model-predicted genes are enriched for \textit{Neuronal System} processes, consistent with the role of synaptic, neuronal, and neurochemical dysregulation in bipolar disorder pathophysiology.& Grande et al., 2016; Fornito et al., 2015 \\
	\hline
	Drug-induced liver disease (C0860207) & Liver carcinoma (DisGeNET) & The prioritized gene set showed significant enrichment for \textit{Liver carcinoma}, suggesting that the model captures hepatic disease-related gene modules and shared molecular mechanisms linking drug-induced liver injury and hepatocarcinogenesis. & Zimmerman, 2000; Stravitz \& Lee, 2019 \\
	\hline
	Depressive disorder (C0011581) & GPCR Downstream Signalling (Reactome) & The prioritized genes are significantly enriched for GPCR downstream signalling, consistent with the central role of GPCR-mediated neurotransmission, including GABAergic signaling, in depression pathophysiology. These pathways are implicated in mood regulation, synaptic plasticity, and treatment response. & Krystal et al., 2019; Luscher et al., 2011 \\
	\hline
	Chronic alcoholic intoxication (C0001973) & Signaling by GPCR (Reactome) & The model-predicted genes were significantly enriched for \textit{Signaling by GPCR}, consistent with the central role of GPCR- and neurotransmitter-mediated signaling in alcohol-related neurobiological and systemic damage. This is in line with studies highlighting the impact of alcohol on neuronal signaling pathways and reward-related circuitry. &  Gołaszewski et al., 2026; Spanagel, 2009\\
\end{longtable}



\begin{thebibliography}{}
	
	% حذف برچسب شماره از کناره مراجع (اختیاری)
	\makeatletter
	\def\@biblabel#1{} 
	\makeatother
	

	\bibitem{seeler2017}
	Seeler, J. S., \& Dejean, A. (2017).
	SUMO and the robustness of cancer.
	\textit{Nature Reviews Cancer}, 17(3), 184--197. doi:10.1038/nrc.2016.143
	
	\bibitem{hendriks2016}
	Hendriks, I. A., \& Vertegaal, A. C. O. (2016).
	A comprehensive compilation of SUMO proteomics.
	\textit{Nature Reviews Molecular Cell Biology}, 17(9), 581--595. doi:10.1038/nrm.2016.81
	
	\bibitem{owen2016}
	Owen, M. J., Sawa, A., \& Mortensen, P. B. (2016).
	Schizophrenia.
	\textit{The Lancet}, 388(10039), 86--97. doi:10.1016/S0140-6736(15)01121-6
	
	\bibitem{kahn2015}
	Kahn, R. S., Sommer, I. E., Murray, R. M., Meyer-Lindenberg, A., Weinberger, D. R., Cannon, T. D., ... \& Insel, T. R. (2015).
	Schizophrenia.
	\textit{Nature Reviews Disease Primers}, 1, 15067. doi:10.1038/nrdp.2015.67
	
	
	\bibitem{bataller2005liver}
	Bataller, R., \& Brenner, S. L. (2005).
	Liver fibrosis.
	\textit{The Journal of Clinical Investigation}, 115(2), 209--218. doi:10.1172/JCI24282
	
	
	\bibitem{kisseleva2021}
	Kisseleva, T., \& Brenner, D. A. (2008).
	Fibrogenesis of parenchymal organs.
	\textit{The FEBS Journal}, 288(5), 1197--1212. doi:10.1513/pats.200711-168DR
	
	\bibitem{fearon1990}
	Fearon, E. R., \& Vogelstein, B. (1990).
	A genetic model for colorectal tumorigenesis.
	\textit{Cell}, 61(5), 759--767. doi:10.1016/0092-8674(90)90186-I
	
	\bibitem{liebl2021}
	Liebl, M. C., \& Hofmann, T. G. (2021).
	The Role of p53 Signaling in Colorectal Cancer.
	\textit{Cancers}, 13(9), 2125. doi:10.3390/cancers13092125
	
	
	\bibitem{drake2014}
	Drake, C. G., Lipson, E. J., \& Brahmer, J. R. (2014).
	Breathing new life into immunotherapy: review of melanoma, lung and kidney cancer.
	\textit{Nature Reviews Clinical Oncology}, 11(1), 24--37. doi:10.1038/nrclinonc.2013.208
	
	
	\bibitem{sfanos2012}
	Sfanos, K. S., \& De Marzo, A. M. (2012).
	Prostate cancer and inflammation: the evidence.
	\textit{Histopathology}, 60(1), 199--215. doi:10.1111/j.1365-2559.2011.04033.x
	

	\bibitem{mossink2021}
	Mossink, B., van Rhijn, J. R., van de疏, S., Schubert, D., \& Schenck, A. (2021).
	The emerging role of chromatin remodelers in neurodevelopmental disorders: a developmental perspective.
	\textit{Cellular and Molecular Life Sciences}, 78(6), 2517--2563. doi:10.1007/s00018-020-03714-5
	
	
	\bibitem{ciptasari2020}
	Ciptasari, U., \& van Bokhoven, H. (2020).
	The phenomenal epigenome in neurodevelopmental disorders.
	\textit{Human Molecular Genetics}, 29(R1), R42--R50. doi:10.1093/hmg/ddaa175
	
	
	\bibitem{grande2016}
	Grande, I., Berk, M., Birmaher, B., \& Vieta, E. (2016).
	Bipolar disorder.
	\textit{The Lancet}, 387(10027), 1561--1572. doi:10.1016/S0140-6736(15)00241-X
	
	
	\bibitem{fornito2015}
	Fornito, A., Zalesky, A., \& Breakspear, M. (2015).
	The connectomics of brain disorders.
	\textit{Nature Reviews Neuroscience}, 16(3), 159--172. doi:10.1038/nrn3901
	
	
	\bibitem{zimmerman2000}
	Zimmerman, H. J. (2000).
	Drug-induced liver disease.
	\textit{Clinical Liver Disease}, 2(2), 39--41. doi:10.1016/s1089-3261(05)70097-0
	
	\bibitem{stravitz2019}
	Stravitz, R. T., \& Lee, W. M. (2019).
	Acute liver failure.
	\textit{The Lancet}, 394(10201), 869--881. doi:10.1016/S0140-6736(19)31894-X
	
	\bibitem{krystal2019}
	Krystal, J. H., Abdallah, C. G., Sanacora, G., Charney, D. S., Duman, R. S., \& Gordon, J. (2020).
	Ketamine: a paradigm shift for depression research and treatment.
	\textit{Neuron}, 101(5), 774--778. doi:10.1016/j.neuron.2019.02.005
	
	\bibitem{luscher2011}
	Luscher, B., Shen, Q., \& Sahir, N. (2011).
	The GABAergic deficit hypothesis of major depressive disorder.
	\textit{Molecular Psychiatry}, 16(4), 383--406. doi:10.1038/mp.2010.120
	
	\bibitem{golaszewski2026}
	Go{\l}aszewski, P., Wawrzyniak, A., K{\l}osowicz, M., Burbelka, A., \& Balawender, K. (2026).
	Neurotoxicity of Chronic Alcohol Exposure: Mechanistic Insights, Cellular Disruption, and Emerging Therapeutic Strategies.
	\textit{International Journal of Molecular Sciences}, 27(1), 299. doi:10.3390/ijms27010299 
	
	\bibitem{spanagel2009}
	Spanagel, R. (2009).
	Alcoholism: a systems approach from molecular physiology to addictive behavior.
	\textit{Physiological Reviews}, 89(2), 649--705. doi:10.1152/physrev.00013.2008
	
	




	
	
\end{thebibliography}



\end{document}