A Non-negative Matrix Factorization Model With Sparse Constraint And Its Initialization

As a technology for obtaining low dimensional representation of extremely high dimension data, nonnegative matrix factorization has a wide applications. For the nonnegative constraint on the solution and additive decomposition, NMF always creates parts-based representations, so in reality to have a good physical meaning. This gave rise to widespread concern about the kind of problem, de-veloped a series of algorithms, from the initial iteration of multiplication to the second-order optimization. They show different performance in convergence rate and the approximation. Taking into account the different statistical properties of data, the model can also be combined with different objective functions, adding a variety of regular constraints, to achieve the solution of specific problems. In addition, the solution of the problem is not unique, the initial value selection has different strategies.In this paper, a brief introduction about the back ground and the existing re-search work are given,then we reviewed the various types of non-negative matrix factorization algorithm, to articulate their ideas and algorithm implementation process. After that, we focus on the existing model named GNMF, add to it a sparse regular items, and the corresponding formulas are derived. We investi-gate the model we gotten in the experiment part. Finally, we compare several initialization strategies.