\vspace{-1em}
\section{Conclusion}


% This paper introduced a novel optimization-based algorithm, the Label-Aware Graph Coarsening (LAGC) algorithm, designed to learn a high-quality coarsened graph. LAGC is the first method to leverage the original graph, the Laplacian matrix, the feature matrix, and some node labels to learn the coarsened graph. The proposed formulation is nonconvex, and solved efficiently using the Block Successive Upper Bound Minimization technique. The LAGC algorithm is proven to be convergent. Its efficacy is demonstrated in downstream node classification tasks, where LAGC consistently outperforms state-of-the-art methods.
This paper introduces the Label-Aware Graph Coarsening (LAGC) algorithm, an optimization-based approach that uniquely incorporates the graph matrix, feature matrix, and label matrix of the original graph for coarsening, marking the first algorithm to consider the label matrix during this process. The method, efficiently solved through block successive upper bound minimization (BSUM), iteratively updates variables while ensuring convergence. Extensive experimentation demonstrates LAGC's superior performance in node classification tasks compared to state-of-the-art methods, establishing a significant advancement in graph coarsening techniques. LAGC's contributions include a comprehensive optimization strategy, an efficient algorithm, and empirical evidence highlighting its practical advantages in enhancing graph-based analyses.