Non-negative matrix factorization (NMF), a method for finding parts-based representation of non-negative data, has shown remarkable competitiveness in data analysis. Given that real-world datasets are often comprised of multiple features or views which describe data from various perspectives, it is important to exploit diversity from multiple views for comprehensive and accurate data representations. Moreover, real-world datasets often come with high-dimensional features, which demands the efficiency of low-dimensional representation learning approaches. To address these needs, we propose a diverse NMF (DiNMF) approach. It enhances the diversity, reduces the redundancy among multiview representations with a novel defined diversity term and enables the learning process in linear execution time. We further propose a locality preserved DiNMF (LP-DiNMF) for more accurate learning, which ensures diversity from multiple views while preserving the local geometry structure of data in each view. Efficient iterative updating algorithms are derived for both DiNMF and LP-DiNMF, along with proofs of convergence. Experiments on synthetic and real-world datasets have demonstrated the efficiency and accuracy of the proposed methods against the state-of-the-art approaches, proving the advantages of incorporating the proposed diversity term into NMF.

中文翻译：

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用于多视图数据表示的多种非负矩阵分解

非负矩阵分解（NMF）是一种用于查找基于零件的非负数据表示的方法，在数据分析中显示出显着的竞争力。鉴于现实世界的数据集通常由多个功能或视图组成，这些功能或视图从各个角度描述了数据，因此重要的是利用多个视图的多样性来获得全面而准确的数据表示。此外，现实世界的数据集通常具有高维特征，这要求低维表示学习方法的效率。为了满足这些需求，我们提出了一种多样化的NMF（DiNMF）方法。它使用新颖的已定义分集项增强了分集，减少了多视图表示之间的冗余，并使学习过程可以线性执行。我们进一步提出了一种局部保留的DiNMF（LP-DiNMF），用于更精确的学习，它确保了来自多个视图的多样性，同时保留了每个视图中数据的局部几何结构。为DiNMF和LP-DiNMF导出了有效的迭代更新算法，以及收敛证明。在合成数据集和真实数据集上进行的实验证明了所提出方法相对于最新方法的效率和准确性，证明了将所提出的多样性项纳入NMF的优势。