Non-negative matrix factorization (NMF) has recently attracted much attention due to its good interpretation in perception science and widely applications in various fields. In this paper, a novel graph regularized NMF algorithm called NMF with locality constrained adaptive graph (NMF-LCAG) is proposed. Compared with other NMF based algorithms, the proposed NMF-LCAG algorithm has the following advantages: 1) Unlike the traditional NMF method which neglects the geometric information of original data, the proposed algorithm introduces a locality constrained graph to discover the latent manifold structure of the data and 2) Different from most graph regularized NMF algorithms in which the graphs are predefined and kept unchanged during the NMF procedure, two locality constraint terms are employed in our NMF-LCAG to adaptively optimize the graph. Thus, the weight matrix of graph and low dimensional features of data can be simultaneously learned by our algorithm, which makes NMF-LCAG more flexible than other approaches. Moreover, an iterative updating strategy is developed to optimize the objective function of our algorithm and the convergence analysis is also given. Extensive experiments are conducted on four face image databases and three UCI datasets to demonstrate the effectiveness of the proposed NMF-LCAG algorithm. Compared with some other related algorithms, the proposed NMF-LCAG algorithm can achieve at least 1% ~ 3% accuracy improvement in most cases.

中文翻译：

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具有局部约束自适应图的非负矩阵分解

非负矩阵分解（NMF）因其在感知科学中的良好解释和在各个领域的广泛应用而最近引起了广泛关注。在本文中，提出了一种新的图正则化 NMF 算法，称为具有局部约束自适应图的 NMF（NMF-LCAG）。与其他基于 NMF 的算法相比，所提出的 NMF-LCAG 算法具有以下优点： 1) 不同于传统的 NMF 方法忽略原始数据的几何信息，所提出的算法引入了局部约束图来发现潜在流形结构的潜在流形结构。 2) 与大多数图正则化 NMF 算法不同，在大多数图正则化 NMF 算法中，图是预定义的并在 NMF 过程中保持不变，我们的 NMF-LCAG 中使用了两个局部约束项来自适应优化图。因此，我们的算法可以同时学习图的权重矩阵和数据的低维特征，这使得 NMF-LCAG 比其他方法更灵活。此外，开发了一种迭代更新策略来优化我们算法的目标函数，并给出了收敛性分析。在四个人脸图像数据库和三个 UCI 数据集上进行了大量实验，以证明所提出的 NMF-LCAG 算法的有效性。与其他一些相关算法相比，本文提出的 NMF-LCAG 算法在大多数情况下可以实现至少 1%~3% 的精度提升。开发了一种迭代更新策略来优化我们算法的目标函数，并给出了收敛性分析。在四个人脸图像数据库和三个 UCI 数据集上进行了大量实验，以证明所提出的 NMF-LCAG 算法的有效性。与其他一些相关算法相比，本文提出的 NMF-LCAG 算法在大多数情况下可以实现至少 1%~3% 的精度提升。开发了一种迭代更新策略来优化我们算法的目标函数，并给出了收敛性分析。在四个人脸图像数据库和三个 UCI 数据集上进行了大量实验，以证明所提出的 NMF-LCAG 算法的有效性。与其他一些相关算法相比，本文提出的 NMF-LCAG 算法在大多数情况下可以实现至少 1%~3% 的精度提升。