中文说明：应用背景1999 年D. D. Lee 和H. S. Seung [26, 27] 在Nature上提出了一种新的矩阵分 解思想—非负矩阵分解(Non-negative Matrix Factorization, NMF). 该文章的发 表迅速引起了各个学术领域研究人员的重视: 一方面, 科学研究中的很多大规模 数据的分析方法需要通过矩阵形式进行有效处理, 而NMF 思想恰好为人类处理 大规模数据提供了一种新的途径; 另一方面, NMF 分解算法相较于传统的一些算 法而言, 具有实现上的简便性, 分解形式和分解结果上的可解释性, 以及占用存储 空间少等诸多优点. 正因为NMF 的这些良好的特点, 使得NMF 在诸多领域都得 到了广泛的应用, 包括: 文本分析与聚类, 数字水印, 人脸检测与识别, 图像检索, 图像复原, 语言建模, 声源分类, 音乐信号分析与乐器识别, 盲信号分离, 网络安 全, 基因及细胞分析等的研究中. 关键技术NMF 解决的是下面的问题, 给定非负矩阵V ∈ R m×n , 求解两个非负子矩 阵W ∈ R m×r 和H ∈ R r×n , 使得 V ≈ W H. 一般情况下r min{m,n}, 从而达到降低数据存储维数的效果. NMF 在Euclidian 距离下的数学模型定义如下, min D F (W, H) = 1 2 V − W H 2 F s.t. W ≥ 0, H ≥ 0.
English Description：
Application background1999 D. Lee H. and S. Seung [26 27], D. on the Nature proposed a new matrixMatrix Factorization (NMF), which is a solution to the thought of the thought, the non negative matrix factorization (Non-negative).Table quickly attracted the attention of researchers in various academic fields: on the one hand, many large scale of scientific researchThe analysis method of data needs to be processed by the matrix form, and the NMF idea is just for the treatment of human beings.Large scale data provided a new approach; on the other hand, the NMF decomposition algorithm is compared with some traditional algorithms.In the case of the method, it has the convenience of realization, the interpretation of the form and the result of decomposition, and the occupancy of the memory.Such a lot of advantages, such as NMF, is because of the good characteristics of NMF, which makes the in many areasTo a wide range of applications, including: text analysis and cluster