Graphical interpretation of non-negative factorization expecting bio-Raman research

Abstract

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.

Bio-Raman non-negative matrix factorization: its practical methodology

“…Let us exemplify the 100 run NMF approach using randomness for initial settings to give possible ranges close to the truths (100 run NMF approach). 18) Figure 1(a) shows simulated binary spectral components, A 1 (ν) and A 2 (ν) (the third spectral component, A 3 (ν), is used later for further discussion), where ν is the spectral variable such as Raman shift. For the discrete expression of ν, dimensionless ordinary numbers, i = 1, 2, … l = 51 are used; e.g, A 1 (ν) can be written A 1 (i).…”

“…In these respects, it has been practically impossible for researchers to directly analyze bio-Raman data; to solve this, advanced spectral analytical methods have been proposed and applied. [8][9][10][11][12][13][14][15][16][17][18][19] The non-negative matrix factorization (NMF) is an effective method to disentangle the complicated and largely sized bio-Raman data. 20,21) Principal component analysis (PCA) is not chemically meaningful including negative values in the loading spectra (i.e., decomposed spectral components); whereas NMF is more meaningful due to the non-negativity of the data.…”

“…But one of the stagnations is 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. In the preceding publication, 18) we graphically found the "possible ranges" close to the truths, by using randomness for initial settings in a binary system and by the 100 runs of projections of the NMF vectors onto the principal component (PC) plane. This 100 run approach began to clarify the mechanism of NMF and opened new viewpoints; yet the strategy for practical use was not described.…”

Principal component analysis for the protein amide I region of Raman imaging data before/after straight perm of human grey hair

“…[1][2][3] Among these analytical techniques, Raman spectroscopy is one of powerful and versatile techniques, as this approach is non-labelling, non-destructive to living tissues / cells, and less influenced by water. As Raman data of a biological tissue is usually complicated and large, techniques for spectral pre-treatments 4,5 and advanced spectral analytical methods, such as principal component analysis (PCA) and non-negative matrix factorization (NMF), 6,7 have been developed and applied.…”

Realization of bio-Raman black hair analysis by automatic signal separation of melanin from other hair components

“…7,8 Bio-Raman data is usually large and the number of spectra frequently reaches thousands. 9,10 Spectral analysis, such as automatic baseline correction, 11 automatic background removal, 12,13 principal component analysis (PCA), 9 non-negative matrix factorization, [14][15][16] and time-series correlation analysis, 17 have been frequently used and sophisticated to extract and visualize intrinsic information.…”