Non-negative matrix factorization algorithm for the deconvolution of one dimensional chromatograms

In chromatogram analysis, overlapped chromatograms are difficult to analyze if they are not resolved. The conventional multivariate resolution techniques do not give accurate results when the chromatograms are severely overlapped. In this work, ML-NMFdiv, modified non-negative matrix factorization (NMF) with divergence objective algorithm has been proposed for the separation of severely overlapped chromatograms of acetone and acrolein mixture. Before applying NMF, principal component analysis (PCA) is applied to determine number of components in the mixture taken. Most of the NMF algorithms used so far for chromatogram separation do not converge to a stable limit point and no uniqueness in the results. To get unique results, instead of random initialization, three different initialization methods namely, Robust initialization, NNDSVD (Non-Negative Double Singular Value Decomposition) based initialization and EFA (Evolving Factor Analysis) based initializations, have been used in this work and the performances are compared. The multiplicative update of already existing NMFdiv algorithm has been modified and proposed in this work as ML-NMFdiv (NMFdiv with modified multiplicative update) for overlapped chromatogram separation to improve the convergence. The proposed ML-NMFdiv algorithm is applied on the simulated and experimental chromatograms obtained for acetone and acrolein mixture. The results of proposed ML-NMFdiv are compared with existing Multivariate Curve Resolution-Alternating Least Square (MCR-ALS) method.