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\begin{document}
\title{Optimization Framework for Semi-supervised Attributed Graph Coarsening }

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\author[*,1]{Manoj Kumar}
\author[*,1]{Subhanu Halder}
\author[2]{Archit Kane}
\author[2]{Ruchir Gupta}
\author[1]{Sandeep Kumar}

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\affil[1]{%
    Dept. of Electrical Engineering\\
    Indian Institute of Technology Delhi\\
    India
}
\affil[2]{%
    Dept. of Computer Science and  Engineering\\
    Indian Institute of Technology (BHU) Varanasi\\
    India
}  
\maketitle 
\def\thefootnote{*}\footnotetext{These authors contributed equally to this work}
\begin{abstract}
In data-intensive applications, graphs serve as foundational structures across various domains. However, the increasing size of datasets poses significant challenges to performing downstream tasks. To address this problem, techniques such as graph coarsening, condensation, and summarization have been developed to create a coarsened graph while preserving important properties of the original graph by considering both the graph matrix and the feature or attribute matrix of the original graph as inputs. However, existing graph coarsening techniques often neglect the label information during the coarsening process, which can result in a lower quality coarsened graph and limit its suitability for downstream tasks.  To overcome this limitation, we introduce the Label-Aware Graph Coarsening (LAGC) algorithm, a semi-supervised approach that incorporates the graph matrix, feature matrix, and some of the node label information to learn a coarsened graph. Our proposed formulation is a non-convex optimization problem that is efficiently solved using  block successive upper bound minimization(BSUM) technique, and it is provably convergent. Our extensive results demonstrate that the LAGC algorithm outperforms the existing state-of-the-art method by a significant margin.
\end{abstract}










\input{001introduction}
\input{002Background and Problem Formulation}
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\section{acknowledgements}
We would like to thank the editor and reviewers for their suggestions to improve this paper.
We would also like to thank to Mr. Prakash Pal for his contribution to
the discussions regarding the paper and code implementation. This work is supported by
the DST Inspire faculty grant MI02322G.

						 
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\title{Supplementary Material}
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\appendix
\input{008Proof of Lemma }
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