# Late Fusion Multi-view Clustering via Global and Local Alignment Maximization

**Authors:** Siwei Wang, Xinwang Liu, En Zhu  
**arXiv:** [2208.01198](https://arxiv.org/abs/2208.01198)  
**Date:** 2022-08-02  
**Summary page:** https://www.summarizepaper.com/en/paper/2208.01198v1/

## Key points

- Multi-view clustering (MVC) combines information from multiple views to improve clustering performance
- Existing approaches often fuse pre-specified similarities, leading to complicated optimization and high computational costs
- The authors propose a late fusion MVC method called LF-MVC-GAM that optimally fuses multiple source information at the partition level and aligns the consensus partition with weighted base partitions
- LF-MVC-LAM is another variant that preserves the local intrinsic structure among multiple partition spaces
- Two three-step iterative algorithms are developed to solve the resulting optimization problems with guaranteed convergence
- Extensive experiments on eighteen multi-view benchmark datasets demonstrate the effectiveness and efficiency of LF-MVC-GAM and LF-MVC-LAM
- The proposed methods offer a promising approach for integrating complementary information from different views to improve clustering performance while reducing computational complexity
- Codes for LF-MVC-GAM and LF-MVC-LAM are publicly available at https://github.com/wangsiwei2010/latefusionalignment
- The work was supported by various funding sources including the National Key R&D Program of China 2020AAA0107100, Natural Science Foundation of China (project no 61922088, 61773392, and 61976196), and Outstanding Talents of “Ten Thousand Talents Plan” in Zhejiang Province (project no 2018R51001)

## Summary

Multi-view clustering (MVC) is a technique that combines information from multiple views to improve clustering performance. However, existing approaches often fuse pre-specified similarities, leading to complicated optimization and high computational costs. In this paper, the authors propose a late fusion MVC method called LF-MVC-GAM that addresses these issues. The authors first establish a theoretical connection between k-means clustering and the alignment between base partitions and the consensus partition. Based on this observation, LF-MVC-GAM optimally fuses multiple source information at the partition level from each view and maximally aligns the consensus partition with these weighted base partitions. This alignment helps integrate partition-level information and simplifies the optimization procedure, reducing computational complexity. To further enhance clustering performance, the authors introduce another variant called LF-MVC-LAM. This variant preserves the local intrinsic structure among multiple partition spaces. The authors then develop two three-step iterative algorithms to solve the resulting optimization problems with guaranteed convergence. Additionally, they provide a generalization error bound analysis of their proposed algorithms. The effectiveness and efficiency of LF-MVC-GAM and LF-MVC-LAM are demonstrated through extensive experiments on eighteen multi-view benchmark datasets, ranging from small to large scale data items. In addition to existing studies on multi-view clustering [41–45], the authors mention a three step alternate algorithm proposed in [46] that jointly optimizes clustering, kernel coefficients, and dimension reduction. They also refer to a multiple kernel k means clustering algorithm with matrix induced regularization. Overall, the proposed late fusion MVC methods offer a promising approach for integrating complementary information from different views to improve clustering performance while reducing computational complexity. The codes for LF–MVC–GAM and LF–MVC–LAM are publicly available at https://github.com/wangsiwei2010/latefusionalignment . Acknowledgments: This work was supported by various funding sources including the National Key R&D Program of China 2020AAA0107100 , Natural Science Foundation of China (project no 61922088 , 61773392 , and 61976196 ), and Outstanding Talents of “Ten Thousand Talents Plan” in Zhejiang Province (project no 2018R51001 ).