Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden dat...

Integrative clustering of multi-level ‘omic data based on non-negative matrix factorization algorithm

Integrative analyses of high-throughput 'omic data, such as DNA methylation, DNA copy number alteration, mRNA and protein expression levels, have created unprecedented opportunities to understand the molecular basis of human disease. In particular, integrative analyses have been the cornerstone in the study of cancer to determine molecular subtypes within a given cancer. As malignant tumors wit...

Non-negative matrix factorization

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...