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A mathematical comparison of non-negative matrix factorization related methods with practical implications for the analysis of mass spectrometry imaging data
Rapid Communications in Mass Spectrometry  (IF2.419),  Pub Date : 2021-08-09, DOI: 10.1002/rcm.9181
Melanie Nijs, Tina Smets, Etienne Waelkens, Bart De Moor

Non-negative matrix factorization (NMF) has been used extensively for the analysis of mass spectrometry imaging (MSI) data, visualizing simultaneously the spatial and spectral distributions present in a slice of tissue. The statistical framework offers two related NMF methods: probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA), which is a generative model. This work offers a mathematical comparison between NMF, PLSA, and LDA, and includes a detailed evaluation of Kullback–Leibler NMF (KL-NMF) for MSI for the first time. We will inspect the results for MSI data analysis as these different mathematical approaches impose different characteristics on the data and the resulting decomposition.