Nonnegative Matrix Factorization With Sparseness Constraint

Nonnegative Matrix Factorization (NMF) is a new proposed method of matrix factorization. Compared with other matrix factorization methods, the special about NMF is by adding nonnegative constraint into matrix factorization the original data will be parts-based represented, which will reflects the local features in a better way. As a matter of fact that most of the experimental data in the real world are nonnegative, this method has found a variety of real world applications in the areas such as blind separation of image and nonnegative signals, pattern recognition, text mining, digital water-marking and facial expression recognition and so on. Depending on an application, the estimated factors may have different interpretation. For example, Lee and Seung introduced NMF as a method for decomposing an image (face) into parts-based representations (such as lips,eyes,nose,ears,etc.).In the first section, we introduce the background of how NMF generates, the discription of the NMF problem, and the research status. We also state some shortcomings and difficluties still existed in the NMF problem.In the second section, we firstly introduce preliminaries, then we state some existing NMF methods in detail, which will give readers a further understanding for NMF.We propose the core of this article in the third section:Nonnegative Matrix Factorization with Sparseness Constraint. This is an improved algorithm. The objective of NMF is to decompose the original Matrix V∈Rm×n into the product of W∈Rm×r and H∈Rr×n, V≈WH, where r satisfies (m+n)r