Unsupervised and semi-supervised fuzzy modularity clustering via multi-view affinity fusion

In recent years, fuzzy modularity clustering has gained widespread attention owing to its alignment with evaluation criteria and learning objective, as well as its robust adaptability to noisy data. However, existing fuzzy modularity clustering methods rely solely on a single distance-based metric to construct the initial affinity graphs, which imposes strong assumptions about the intrinsic data distribution and leads to inferior clustering performance in real-world applications. To address this limitation, this study introduces the concept of the multi-view affinity graph, which is free from the constraints of any single metric. We further employ an affinity fusion technique to integrate initial graphs from multiple views, allowing the combined graph to simultaneously reflect the characteristics of diverse metrics. Subsequently, the notion of fuzzy modularity is adopted to formulate the learning objective, and a novel clustering method called Fuzzy Modularity Clustering via Multi-view Affinity Fusion (FMC-MAF) is proposed. Moreover, the semi-supervised learning variant, sFMC-MAF, is also developed to effectively utilize labeled samples while introducing only one additional hyperparameter and maintaining the optimization framework. Extensive experiments on both synthetic and real-world benchmark datasets demonstrate the effectiveness of both the proposed FMC-MAF and sFMC-MAF.