Nonnegative matrix factorization (NMF) is an effective technique to extract the underlying low-dimensional structure of data by utilizing its parts-based representation, which has been widely used in feature extraction and machine learning. However, NMF is an unsupervised learning algorithm without utilizing the discriminative prior information. In this paper, we put forward a new class-driven NMF with manifold regularization (MCDNMF) algorithm, which incorporates both the local manifold regularization and the label information of data into the NMF model. Specifically, MCDNMF not only encodes the local geometrical structure of data space by using the manifold regularization, but also takes the available label information by introducing the class-driven constraint. This class-driven constraint forces the new representations of data points to be more similar within the same class while different between other classes. Therefore, the discriminative abilities of clustering are greatly boosted. Experimental results on several datasets validate the effectiveness of proposed MCDNMF in comparison with the other state-of-the-art methods.

中文翻译：

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用于数据聚类的具有流形正则化的类驱动非负矩阵分解


非负矩阵分解（NMF）是一种利用其基于部分的表示来提取数据底层低维结构的有效技术，已广泛应用于特征提取和机器学习中。然而，NMF 是一种无监督学习算法，没有利用判别性先验信息。在本文中，我们提出了一种新的带有流形正则化的类驱动NMF（MCDNMF）算法，该算法将局部流形正则化和数据的标签信息结合到NMF模型中。具体来说，MCDNMF不仅利用流形正则化对数据空间的局部几何结构进行编码，而且通过引入类驱动约束来获取可用的标签信息。这种类驱动的约束迫使数据点的新表示在同一类内更加相似，而在其他类之间则不同。因此，聚类的判别能力大大提高。多个数据集上的实验结果验证了所提出的 MCDNMF 与其他最先进方法相比的有效性。