Multi-view clustering has attracted increasing attention in recent years since many real data sets are usually gathered from different sources or described by different feature types. Amongst various existing multi-view clustering algorithms, those that are based on non-negative matrix factorization (NMF) have exhibited superior performance. However, NMF decomposing original data directly fails to exploit global relationships between data samples and cannot be applied to datasets that are not strictly non-negative. In this paper, a network-based sparse and multi-manifold regularized multiple NMF (NSM_MNMF) for multi-view clustering is proposed, where multi-view data is transformed into multiple networks, and NMF is used to jointly factorize transformed multiple networks for capturing the shared cluster structure embedded in different views. Furthermore, sparse and multi-manifold regularization are incorporated into NMF to keep the intrinsic geometrical information of the multi-view network manifold space. Networks characterize intra-view similarity, and joint factorization reveals inter-view similarity across distinct views, while using NMF to decompose the networks instead of the original data means NSM_MNMF can be applied to datasets that are not strictly non-negative and the clustering results are interpretable. Extensive experiments are conducted on nine real data sets to assess the method proposed, and the results illustrate that NSM_MNMF outperforms other baseline approaches.

近年来，由于许多实际数据集通常是从不同来源收集或由不同要素类型描述的，因此多视图聚类已引起越来越多的关注。在各种现有的多视图聚类算法中，基于非负矩阵分解（NMF）的算法表现出了卓越的性能。但是，NMF直接分解原始数据无法利用数据样本之间的全局关系，因此不能应用于严格非负数的数据集。本文提出了一种基于网络的稀疏和多流形正则化多NMF（NSM_MNMF）的多视图聚类算法，该方法将多视图数据转换为多个网络，并使用NMF联合分解转换后的多个网络进行捕获。嵌入在不同视图中的共享群集结构。此外，稀疏和多流形正则化被合并到NMF中，以保留多视图网络流形空间的固有几何信息。网络表征了视图内相似性，联合分解揭示了不同视图之间的视图间相似性，同时使用NMF分解网络而不是原始数据，这意味着NSM_MNMF可以应用于并非严格非负的数据集，并且聚类结果是可解释的。在9个真实数据集上进行了广泛的实验，以评估所提出的方法，结果表明NSM_MNMF优于其他基准方法。联合分解揭示了不同视图之间的视图间相似性，同时使用NMF分解网络而不是原始数据意味着NSM_MNMF可以应用于并非严格非负且聚类结果可解释的数据集。在9个真实数据集上进行了广泛的实验，以评估所提出的方法，结果表明NSM_MNMF优于其他基准方法。联合分解揭示了不同视图之间的视图间相似性，同时使用NMF分解网络而不是原始数据意味着NSM_MNMF可以应用于并非严格非负且聚类结果可解释的数据集。在9个真实数据集上进行了广泛的实验，以评估所提出的方法，结果表明NSM_MNMF优于其他基准方法。