Survey on the Variations and Applications of Nonnegative Matrix Factorization

Nonnegative Matrix Factorization has been proved to be valuable in many fields of data mining, especially in unsupervised learning. In this paper, we will briefly review its variations and applications in image processing, data clustering, semi-supervised clustering, bi-clustering (co-clustering) and financial data mining. Note that we cannot cover all the interesting works on NMF, but generally speaking, the special point on NMF is its ability to recover the hidden patterns or trends behind the observed data automatically, which makes it suitable for image processing, feature extraction, dimensional reduction and unsupervised learning. The preliminary theoretical analysis concerning this ability, in other words, the relations between NMF and some other unsupervised learning models have been studied in ref. [4, 5]. The rest of the paper is organized as follows: Sect. 2 surveys a variety of variations of NMF, Sect. 3 surveys the applications of NMF, and Sect. 4 concludes.