Non-negative Matrix Factorization: A Survey

Literature Survey: Non-Negative Matrix Factorization

This article surveys recent research on Non-Negative Matrix Factorization (NNMF), a relatively new technique for dimensionality reduction. It is based on the idea that in many data-processing tasks, negative numbers are physically meaningless. The NNMF technique addresses this problem by placing non-negativity constraints on the data model. I discuss the applications of NNMF, the algorithms and...

Non-negative matrix factorization

A new approach for building recommender system using non negative matrix factorization method

Nonnegative Matrix Factorization is a new approach to reduce data dimensions. In this method, by applying the nonnegativity of the matrix data, the matrix is ​​decomposed into components that are more interrelated and divide the data into sections where the data in these sections have a specific relationship. In this paper, we use the nonnegative matrix factorization to decompose the user ratin...

Bayesian Non-negative Matrix Factorization

We present a Bayesian treatment of non-negative matrix factorization (NMF), based on a normal likelihood and exponential priors, and derive an efficient Gibbs sampler to approximate the posterior density of the NMF factors. On a chemical brain imaging data set, we show that this improves interpretability by providing uncertainty estimates. We discuss how the Gibbs sampler can be used for model ...

Robust non-negative matrix factorization

Non-negative matrix factorization (NMF) is a recently popularized technique for learning partsbased, linear representations of non-negative data. The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption, and hence not suitable if the data are grossly corrupted. To improve the robustness of NMF, a novel algorithm named robust nonnegative matrix factorization (RNMF) i...