Upper bound of Bayesian generalization error in non-negative matrix factorization

Upper bound of Bayesian generalization error in non-negative matrix factorization

Non-negative matrix factorization ( NMF ) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log c...

Upper Bound of Bayesian Generalization Error in Stochastic Matrix Factorization

Stochastic matrix factorization (SMF) has proposed and it can be understood as a restriction to non-negative matrix factorization (NMF). SMF is useful for inference of topic models, NMF for binary matrices data, and Bayesian Network. However, it needs some strong assumption to reach unique factorization in SMF and also theoretical prediction accuracy has not yet clarified. In this paper, we stu...

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 ...

Soft Partitioning in Networks via Bayesian Non-negative Matrix Factorization

Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilizes the Bayesian non-negative matrix factorization (NMF) model to extract overlapping modules from a network. The scheme has the advantage of computational efficiency, soft community membership and an intuitive foundation. We present the performance of...

Non-negative matrix factorization