Non-negative matrix factorization (NMF) has been frequently used in research on live cells, biomolecules, and tissues (bio-Raman research) to disentangle the complicated and large sized data. A stagnation is that NMF does not provide unique decomposition, depending on initial settings; that is, NMF returns non-negative spectral components close to the truths, but solely giving several possibilities. In this research, we visualized possible ranges of NMF in binary component system. The mechanism of NMF became more clarified and opened new viewpoints.

Research on live cells using a Raman microscope (bio-Raman research) has been attractive due to its versatility; but informative bio-Raman data has been complicated and largely sized. Non-negative matrix factorization (NMF) is expected an effective method to disentangle it; but the problem was that NMF does not give the unique decomposition, depending on different initial settings. That is, NMF causes cross-talks among factorized signals that disturb the quantitative analysis. To exemplify the problem, Raman imaging of a cross section of a rice grain was analyzed. To solve the problem, a practical methodology of bio-Raman NMF was described.