Robust vector-weighted and matrix-weighted multi-view hard c-means clustering

With the rapid advancement of information technology, multi-view data has become ubiquitous, prompting extensive attention towards multi-view clustering algorithms. Despite significant strides, several challenges persist: (1) the prevalence of noise and outliers in real-world multi-view data often compromises the efficacy of clustering; (2) most existing multi-view clustering algorithms predominantly assess the overall contribution of each view, while neglecting the intra-view contributions. In this paper, we first propose a robust vector-weighted multi-view hard c-means (VW-MVHCM) clustering, drawing inspiration from the single- view alternative hard c-means. A distinctive feature of VW-MVHCM is the substitution of the conventional Euclidean norm with a non-Euclidean norm metric, enhancing its resilience to noise and outliers. Additionally, we introduce view weights to learn the contribution of each view in clustering. On this basis, we further propose a robust matrix-weighted multi-view hard c-means (MW-MVHCM) clustering, which assigns view- specific weights at the cluster level, allowing for more detailed intra-view contribution modeling. This matrix-weighted approach enables MW-MVHCM to dynamically capture the varying importance of each view across clusters, improving clustering performance. We design an optimization scheme to obtain the optimal results of VW-MVHCM and MW-MVHCM. Experimental results on benchmark datasets demonstrate that our proposed algorithms outperform existing multi-view clustering algorithms, showcasing their robustness and effectiveness in real-world scenarios.