Functional Biogeography of Ocean Microbes Revealed through Non-Negative Matrix Factorization

Functional Biogeography of Ocean Microbes Revealed through Non-Negative Matrix Factorization

The direct "metagenomic" sequencing of genomic material from complex assemblages of bacteria, archaea, viruses and microeukaryotes has yielded new insights into the structure of microbial communities. For example, analysis of metagenomic data has revealed the existence of previously unknown microbial taxa whose spatial distributions are limited by environmental conditions, ecological competitio...

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...

Non-Negative Multiple Matrix Factorization

Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information inc...