Multi-view clustering has attracted significant attention and application. Nonnegative matrix factorization is one popular feature learning technology in pattern recognition. In recent years, many semi-supervised nonnegative matrix factorization algorithms are proposed by considering label information, which has achieved outstanding performance for multi-view clustering. However, most of these existing methods have either failed to consider discriminative information effectively or included too much hyper-parameters. Addressing these issues, a semi-supervised multi-view nonnegative matrix factorization with a novel fusion regularization (FRSMNMF) is developed in this paper. In this work, we uniformly constrain alignment of multiple views and discriminative information among clusters with designed fusion regularization. Meanwhile, to align the multiple views effectively, two kinds of compensating matrices are used to normalize the feature scales of different views. Additionally, we preserve the geometry structure information of labeled and unlabeled samples by introducing the graph regularization simultaneously. Due to the proposed methods, two effective optimization strategies based on multiplicative update rules are designed. Experiments implemented on six real-world datasets have demonstrated the effectiveness of our FRSMNMF comparing with several state-of-the-art unsupervised and semi-supervised approaches.

多视图聚类引起了人们的广泛关注和应用。非负矩阵分解是模式识别中一种流行的特征学习技术。近年来，许多考虑标签信息的半监督非负矩阵分解算法被提出，在多视图聚类方面取得了优异的性能。然而，大多数现有方法要么未能有效考虑判别信息，要么包含过多的超参数。为了解决这些问题，本文开发了一种具有新型融合正则化的半监督多视图非负矩阵分解（FRSMNMF）。在这项工作中，我们通过设计的融合正则化来统一约束簇之间多个视图和判别信息的对齐。同时，为了有效地对齐多个视图，使用两种补偿矩阵来归一化不同视图的特征尺度。此外，我们通过同时引入图正则化来保留标记和未标记样本的几何结构信息。由于所提出的方法，设计了两种基于乘法更新规则的有效优化策略。在六个真实世界数据集上进行的实验证明了我们的 FRSMNMF 与几种最先进的无监督和半监督方法相比的有效性。