The Rechearch Of Non-Negative Matrix Factorization And Its Application In Chemical Spectra Resolution

The new methodologies are the hot research and drive the evolution of chemometrics.Non-negative Matrix Factorization (NMF), with the constraints of non-negativity, hasbeen recently proposed for multivariate data analysis. Because it allows only additive, notsubtractive, combinations of the original data, NMF is capable of producing region orparts based representation of objects. It has been used for image analysis and textprocessing. Unlike PCA, the resolutions of NMF are non-negative and can be easilyinterpreted and understood directly.The author focuses on the research of the theory and applications of nonnegativematrix factorization (NMF). The work includes the following sections.Firstly, the author investigates the principle and arithmetic of non-negative matrixfactorization. NMF is a method to obtain a representation of data using non-negativityrestraint. An original analytical matrix can be decomposed to two factorization matrices.NMF can directly obtain a representation of nonnegative data by using multiplies updaterules. NMF implementation is based on elements, not on vectors. It is different from theconventional factor analysis. Just due to it, NMF can learn the local representations ofdata, and the factorization results have realistic physical chemistry meaning and can bedirectly understood without additional operations, such as rotation and projection.Secondly, the author does some research on the improvement of NMF algorithmaccording to the properties of chemical signals (such as the unimodality ofchromatograms, etc.). The feasible solution region is narrowed under experimental error.Thirdly, the conditions for the resolution of chemical spectra are also discussed. Boththe simulated data and the analytical data are resolved successfully by the improved NMF.Additionally, the author also compares NMF with another two curve resolutionmethods: heuristic evolving latent projections (HELP) and multivariate curveresolution-alternating least squares (MCR-ALS).