Using semi-nonnegative matrix underapproximation for statistical process monitoring

In this paper, we explore the application of nonnegative matrix factorization (NMF) in statistical process monitoring. NMF has become a famous dimension reduction and feature extraction method due to its ability to produce highly localized, sparse and parts-based representation. However, NMF and all kinds of its variants have to suffer their failure to obtain some kind of statistical property of data. In this paper, semi-NMF, a variant of NMF, is first improved to reduce the correlation of the obtained low-dimensional data using an underapproximation technique called semi-nonnegative matrix underapproximation (semi-NMU). As a result, semi-NMU can extract latent variables with lower correlation and additionally obtain base matrix with higher sparsity and orthogonality. Then semi-NMU is used for fault detection. The monitoring performance of semi-NMU is evaluated by three case studies.