Parameter-Free Dual-Granularity Weighted Multiview Fuzzy $c$-Means Clustering

It remains a challenge in multi-view clustering to effectively integrate heterogeneous views while reducing the impact of noise and redundancy. To tackle this issue, we propose a parameter-free dual-granularity weighted multi-view fuzzy$c$-means clustering framework. The basic idea is to introduce a product-to-one constraint at both the view and attribute levels, enabling adaptive and balanced weight assignment without introducing extra parameters. Two weighting strategies are developed: (i) vector-form weighting, which assigns global importance to views and attributes, and (ii) matrix-form weighting, which further captures cluster-specific relevance. Moreover, both Euclidean and non-Euclidean (exponential transformation) distance measures are incorporated, yielding four algorithmic variants: PDW-MFC-V, PDW-MFC-M, PDW-MAFC-V, and PDW-MAFC-M. Extensive experiments on nine real-world datasets show that our algorithms outperform thirteen related algorithms across multiple metrics. These results confirm that dual-granularity weighting effectively models the relative importance of views and attributes, while the non-Euclidean distance improves robustness to noise. Overall, the proposed framework offers a flexible, parameter-free, and robust solution for multi-view clustering, providing fine-grained interpretability and stable performance across diverse datasets.