Nonnegative Matrix Factorization with Nonlinear Constraints

Abstract

Processing of data with large dimensions has been a hot topic in recent decades. Various techniques have been proposed to execute the desired information or structure. Non- Negative Matrix Factorization-based on non-negatives data has become one of the favorite methods for shrinking dimensions. The main strength of this approach is the non-negative object, the object modeled by a combination of some basic non-negative parts so as to provide a physical interpretation of the object construction. NMF methods include the use of text mining, pattern recognition, and bioinformatics. The mathematical formulation for NMF did not appear as a convex optimization problem, and various types of model mathematics have been proposed to solve the problem Framework for Alternative Nonnegative Least Square. (ANLS) Are coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This dissertation proposes a new algorithm to solve NMF based on the framework ANLS. This algorithm is put forward primary pivot methods to least squares problem with not – negative constraints which can overcome the limitations of the active set method. The proposed algorithm explores the reduced gradient method is a method that efficiently blocks the central pivot in the context of NMF. These algorithms also own ANLS convergence properties of the framework can be developed for the formulations and NMF with other constraints.