# Consensus Guided Multi-View Unsupervised Feature Selection with Hybrid Regularization
## 5 Discussion  
This work introduces a Consensus-Guided Multi-View Unsupervised Feature Selection framework with Hybrid Regularization (CGMvFS). Our methodology formulates unified consensus representations through systematic aggregation of view-specific base  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Handwritten** & **WebKB** & **Yale** & **Outdoor Scene** & **ORL** & **MSRCV1** \\ \hline CCSFS & 268.74 & 9.15 & 138.39 & 256.47 & 275.15 & 3.12 \\ CDMvFS & 938.17 & 4.02 & 138.39 & 1227.69 & 119.69 & 2.65 \\ CGMvFS & 3.76 & 11.34 & 847.02 & 11.88 & 889.06 & 2.1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The runtimes of different methods on different datasets.  
Figure 5: Convergence trajectory analysis: objective function evolution of CGMvFS across iterative refinement stages.  
Figure 6: ACC and NMI results of the influence of Gaussian noise features on CGMvFS.  
partitions, preserving cross-view pairwise constraints to govern the feature selection process. This approach synergistically captures complementary similarity patterns across views while mitigating single-view bias through consensus regularization. The proposed optimization architecture innovatively integrates a dual-norm formulation, combining \(L_{2,1}\)-norm induced feature sparsity with Frobenius norm-based stability enhancement, effectively balancing model fidelity and generalization capacity. Empirical validation across six heterogeneous multi-view benchmark datasets confirms the framework's superiority.  
However, the proposed method exhibits certain limitations: (1) significant scope for computational efficiency enhancement and (2) potential noise susceptibility in consensus clustering derivation through view averaging. Future work will pursue algorithmic refinements to boost computational efficiency and scalability while incorporating adaptive view-specific reliability weighting to enhance real-world applicability.  
Methodology: [PERSON], [PERSON] ([PERSON]) and [PERSON]; validation: [PERSON]. ([PERSON]); writing--original draft preparation: [PERSON]. ([PERSON]); writing--review and editing: [PERSON] and [PERSON]; formal analysis: L.C.; investigation: [PERSON]; data curation: Q.L.; visualization: [PERSON]. ([PERSON]); supervision: [PERSON]; funding acquisition: Y.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China under No. 62306122, the Natural Science Foundation of Xiamen under No. 3502Z202571034, the Natural Science Foundation of Fujian Province under No. 2022J05065, the Fundamental Research Funds for the Central Universities under No. ZQN-1122, the High-level Talent Team Project of Quanzhou City under No. 2023 CT001, the Scientific Research Funds of Huaqiao University under No. 24 BS141, and the Science and Technology Major Special Project of Fujian Province under No. 2024 HZ022007.  
Not applicable.  
The datasets analyzed in this study were derived from Multi-view Unsupervised Feature Selection With Consensus Partition And Diverse Graph [15] (DOI: 10.1016/j.ins.2024.120178.  
We are extremely grateful for the valuable suggestions provided by the editors and reviewers.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.