Nonnegative matrix factorization and its applications in pattern recognition (Q871855)

Nonnegative matrix factorization (NMF) is a multivariate data analysis. Let \(X_{n\times m}\) be a data matrix with \(m\) samples in \(n\)-dimensional space, where all entries are nonnegative. Then \(X_{n\times m}\) can be decomposed into \(X_{n\times m}\approx B_{n\times r}C_{r\times m}\), where \(B_{n\times r}\) is called basis and \(C_{r\times m}\) is called coefficient matrix. Among many other things, the authors develop formulas for noise models and loss functions, they investigate local NMF and nonnegative space coding. They also deal with some practical questions of pattern recognition.