Non-Negative Matrix Factorization And Its Application

As a technology for obtaining low dimensional representation from extremely high dimension data, dimensionality reduction plays an important role in many fields such as pattern recognition, machine learning, independent component analysis(ICA) and image processing, etc. Non-negative matrix factorization (NMF for short), a method of dimension reduction, catches many people's eyes in recent years for its explicit physical meaning and good explication .By the end of factorization, NMF can be classified into two categories : one aim is to discard some fragile information and get some intrinsic information deep in something by mapping the sample points in a high dimension space into a subspace with much lower dimension while reserving certain properties. The other tries to get some properties or strength of latent independent component in an unknown complex system. Therefore, due to the different applying field of NMF, the Imposed strictness and properties to reserve are very different. In this paper , taking ICA and face recognizing experiment for example , we will propose a series of method to enhance the representation of NMF.At first, we will give a brief introduction to the background , academic description and the existing research work of non-negative matrix factorization , then we propose a new kind of sparse measurement of vector, and algorithm to solve the optimal sparse approximation was given, which will be used in the following algorithm named sparse NMF . After this, in the field of face recognizing, we propose the conception of weighted unity and give two kinds of effective approach to compute the weighted coefficient ,by which, we get a great effect in our experiment. Meanwhile , in the field of ICA, we propose a new approach of NMF with shift, which extends the previous NMF to the field without non-negative strictness. Furthermore, we enhance some methods to modify the result, such as stage-extraction and component- smoothness .