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<p>In-processing method for obtaining fair clustering using spectral clustering algorithm was addressed in the literature. Constraints that consider the <i>balance</i> definition are introduced into spectral clustering optimization formulation. In the current research, we propose a pre-processing method for obtaining fair clustering. The graph property namely <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\texttt{homophily}\)</EquationSource> </InlineEquation>, and its inverse relation to <i>balance</i>, is utilized to device a Graph Repair Method (GRM). The proposed GRM accepts a graph and sensitive attribute as inputs, and outputs a modified graph that has low <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\texttt{homophily}\)</EquationSource> </InlineEquation>. The modified graph, when supplied as input to the spectral clustering, results in fair clusters with high <i>balance</i>. We demonstrate that the graphs with low <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\texttt{homophily}\)</EquationSource> </InlineEquation> have high <i>balance</i>. Extensive experimentation shows that GRM is at par with in-process method of fair spectral clustering.</p>

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Graph pre-processing method for fairness in spectral clustering

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Adithya K. Moorthy,
  • V. Vijaya Saradhi,
  • Bhanu Prasad

摘要

In-processing method for obtaining fair clustering using spectral clustering algorithm was addressed in the literature. Constraints that consider the balance definition are introduced into spectral clustering optimization formulation. In the current research, we propose a pre-processing method for obtaining fair clustering. The graph property namely \(\texttt{homophily}\) , and its inverse relation to balance, is utilized to device a Graph Repair Method (GRM). The proposed GRM accepts a graph and sensitive attribute as inputs, and outputs a modified graph that has low \(\texttt{homophily}\) . The modified graph, when supplied as input to the spectral clustering, results in fair clusters with high balance. We demonstrate that the graphs with low \(\texttt{homophily}\) have high balance. Extensive experimentation shows that GRM is at par with in-process method of fair spectral clustering.