Abstract: Abstract: Non-negative Matrix Factorization (NMF), as a commonly used matrix factorization technology, has been widely used in machine learning, pattern recognition and other fields. However, the existing NMF algorithm often designs the objective function based on Euclidean distance, which makes it sensitive to noise. Therefore, in order to enhance the robustness of the algorithm, we propose a new Manifold regularized nonnegative matrix factorization based on clean data (MRNMF/CD) algorithm. In the MRNMF/CD algorithm, low-rank constraints, manifold regularization, and non-negative matrix factorization technologies are seamlessly integrated, which makes the algorithm perform better. First, by imposing low-rank constraints, MRNMF/CD can recover clean data from noisy data and obtain the global structure of the data; secondly, in order to use the local geometric structure information of the data, MRNMF/CD incorporates manifold regularization into the objective function in. In addition, this paper also proposes an iterative algorithm for solving MRNMF/CD, and theoretically analyzes the convergence of the algorithm. Experiments on some data sets show that MRNMF/CD has better performance than some existing algorithms.

Key words: Keywords: Low rank Constraint, Nonnegative matrix factorization (NMF), manifold regularized, Robust, Clean data

摘要： 摘 要: 非负矩阵分解（Non-negative Matrix Factorization，NMF）算法作为一种常用的矩阵分解技术，已被广泛应用于机器学习、模式识别等领域。但是现有的NMF算法往往基于欧式距离来设计目标函数的，使得其对噪声比较敏感。为此，为了增强算法的鲁棒性，本文提出了一种新的基于干净数据的流形正则化非负矩阵分解（Manifold regularized nonnegative matrix factorization based on clean data, MRNMF/CD）算法。在MRNMF/CD算法中，把低秩约束、流形正则化和非负矩阵分解技术无缝地融为一体，使得其算法性能较为优异。首先，通过加以低秩约束，MRNMF/CD可以从噪声数据中恢复干净数据，并获得数据的全局结构；其次，为了利用数据的局部几何结构信息，MRNMF/CD把流形正则化融入到目标函数中。此外，本文还提出了一种求解MRNMF/CD的迭代算法，并从理论上分析了该求解算法的收敛性。在一些数据集上的实验表明，MRNMF/CD比现有的一些算法具有更好的性能。

关键词: 关键词: 低秩约束, 非负矩阵分解（NMF）, 流形正则化, 鲁棒性, 干净数据