Fast Fuzzy Graph Cut for Clustering

Graph clustering typically involves a two-step process: relaxation followed by post-processing. However, it often leads to significant information loss during relaxation and solution deviation in post-processing. Additionally, traditional graph clustering faces computational challenges due to regular graph construction and spectral decomposition, and binary indicators hinder interpretability in uncertain scenarios. We propose a novel method termed Fast Fuzzy Graph Cut (FFGC) to overcome key issues in graph clustering by: preventing information loss by tackling the original graph cut problem; eliminating solution deviation by directly solving for the target variable; alleviating computational burdens by employing anchor graphs in place of regular graphs; and enhancing flexibility by incorporating a regularization term to soften the cluster indicator. The use of a fuzzy cluster indicator within the graph cut framework expands FFGC's applicability to a wider range of real-world data, increasing both its adaptability and interpretability. In addition, we develop two efficient optimization algorithms to solve the resulting objective problem. Extensive experimental evaluations validate the superior efficiency and effectiveness of FFGC in clustering tasks. The code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/caccode/FFGC</uri>.