非负矩阵分解：模型、算法和应用

近年来,非负矩阵分解模型已经成为数据挖掘领域中最成功的模型之一。该模型能够自动从一组高维向量中提取隐含模式,从而被广泛应用于降维、无监督学习（图像处理、聚类和双聚类等）和预测当中。本文将从它的发展历史、数学表达形式、算法和热点应用等几个层面对非负矩阵分解模型进行综述。简言之,该模型具有较好的可解释性,模型简单,易于理解操作,可拓展性强,该模型和无监督学习领域中其它被广泛采用的模型关系紧密,且有广泛的应用空间,数值表现优异。同时作为一项新兴技术,该模型亦有许多有趣的问题值得进一步深入研究。

Nonnegative Matrix Factorization. Model,Algorithms and Applications

Nonnegative Matrix Factorization （NMF） is becoming one of the most popular models in data mining society recently. NMF can extract hidden patterns from a series of high-dimensional vectors automatically, and has been applied for dimensional re duction, unsupervised learning （image processing, clustering and co-clustering, etc. ） and prediction successfully. This paper sur veys NMF in terms of the research history, model formulation, algorithms and applications. In summary, NMF has good interpret ability, is very flexible, has a close relationship with the existing state of the art unsupervised learning models and a variety of appli cations. In addition, as a developing technology, there are still many interesting open issues remained unsolved and waiting for re search from different perspectives.