Application of non-negative matrix factorization combined with Fisherʹs linear discriminant analysis for classification of olive oil excitation–emission fluorescence spectra

Non-negative matrix factorization (NMF) is a technique that decomposes multivariate data into a smaller number of basis functions and encodings using non-negative constraints. These constraints make that only positive solutions can be obtained and thus this method provides a more realistic approximation to the original data than other factorization methods that allow positive and negative values. Here we show that NMF is a powerful technique for learning a meaningful parts-based representation of the fluorescence excitation–emission matrices (EEMs) of different sets of olive oils. The capabilities of NMF used together with Fisherʹs LDA for discriminating between various types of oils were also studied. In all cases, good classifications were obtained (90–100%). The classification results obtained with the proposed method were compared to those obtained using two other classification methods (parallel factor analysis (PARAFAC) combined with Fisherʹs LDA and discriminant multi-way partial least squares regression (DN-PLSR)).