An algorithm for overlapped chromatogram separation

Non-negative matrix factorization (NMF) is a recently developed method for real time data analysis. In the past it has been used for facial recognition and spectral data analysis. Most of the NMF algorithms do not converge to a stable limit point and uniqueness in results is also a problem in NMF. To improve the convergence, a new NMF algorithm with modified multiplicative update (ML-NMFmse) has been proposed in this work for strongly overlapped and embedded chromatograms separation. To get same results for all the runs, instead of random initialization, three different initialization methods have been used namely, ALS–NMF (robust initialization), NNDSVD based initialization and EFA based initializations. The proposed ML-NMFmse algorithm is applied on the simulated and experimental overlapped chromatograms obtained for acetone and acrolein mixture, using Gas Chromatography–Flame Ionization Detector. Before applying NMF, Principal Component Analysis (PCA) was applied to determine number of components in the mixture taken. The result of proposed ML-NMFmse is compared with that of existing Multivariate Curve Resolution-Alternating Least Squares method in optimal conditions for both the algorithms. In the case of embedded chromatogram, the proposed ML-NMFmse with Robust method (ALS-NMF) of initialization performs better than all other methods. For a resolution of severely overlapped chromatograms, the proposed ML-NMFmse with NNDSVD method of initialization outperforms all other methods.