Nonnegative Matrix Factorization (NMF) is a rapidly developing partsbased machine learning algorithm, which can be used as  a tool of dimensionality reduction and can identify the local features for highdimensional data. NMF has a broad application in the analysis and interpretation of biological data, and a number of practical algorithms have been derived from it. This paper systematically analyzes the mathematical foundation of NMF and its advantages for the representation of local features, and surveys the advances of different varieties, initialization and parameter selection for the NMF algorithm. Also, its application in bioinformatics is reviewed and classified into several categories. Finally, the future directions of the NMF research and application are analyzed and predicted.