一种多流形正则化的多视图非负矩阵分解算法  

A multi-manifold regularized multi-view non-negative matrix factorization algorithm

作　　者：宗林林 张宪超[1] 赵乾利 于红[1] 刘馨月[1] 

机构地区：[1]大连理工大学软件学院,大连116620

出　　处：《南京大学学报（自然科学版）》2017年第3期557-568,共12页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(61272374;61300190;61428202);国家高技术研究发展计划(863计划)(2015AA015403)

摘　　要：在大数据时代,多视图数据普遍存在.多视图聚类是分析多视图数据的一种常用方法.基于多流形正则化非负矩阵分解的多视图聚类是一种极具竞争力的多视图聚类算法,但该算法没有考虑非负矩阵分解的簇排列问题,并且在实验中没有考虑每个视图的差异性.基于上述问题,提出一种优化的多流形正则化的多视图非负矩阵分解算法.该算法的关键问题包括如何利用多视图信息聚类以及如何融合多流形.对多视图数据聚类时,令所有视图的数据共享一个低维的子矩阵,并且最小化所有视图的加权目标函数,从而体现每个视图对聚类的重要性并确保所有非负矩阵分解的簇排列的一致性.在融合多流形信息时,使用基于多视图谱聚类的权重计算方法,加权寻找一致的流形,从而体现每个视图中流形的重要性.实验结果表明,提出的优化策略可以提高多视图聚类的效果.In the era of big data, data often comes from multiple feature extractors or consists of multiple views. Multi- view clustering is one of the common approaches for the analysis of such data, which separates data into several groups using information from multiple views. Multi view clustering via multi-manifold regularized non-negative matrix factorization has become one of the most modern multi-view clustering algorithms in the past decade. However, they do not consider the cluster permutation in non-negative matrix factorization, and they equally treat each view in the experiment. Based on the above issues, in this paper, an improved multi-manifold regularized multi-view non-negative matrix factorization algorithm has been proposed. The key problems of this algorithm are the way of clustering multi- view data and the integration of multi-manifold. In the process of clustering multi-view data, the multi-view data share the same low dimensional sub-matrix and the weighted objective function of all views is minimized, which indicates the importance of each view in clustering and ensures the consistency of cluster permutations in non-negative matrix factori zation. In the process of integrating multiple manifolds, the consensus manifold is approximated by the weighted linear combination of multiple manifolds. To show the importance of each view＇s manifold, the weighting schema based on multi view spectral clustering is adopted to find the consensus manifold. To show the effectiveness of the proposed strategy, we experiment on several benchmark datasets. Experimental results show that the proposed algorithm outperforms the state of the art and tbe proposed optimization strategies are effective for multi view clustering.

关 键 词：非负矩阵分解 多视图聚类 多流形 权重 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]