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

Research on live biological tissues, cells and biomolecules using Raman microscope (also known as bio-Raman research) has continued to grow owing to its many contributions in advancing different fields such as medicine. Raman microscope is widely used in this research due to its numerous benefits, including non-destructive and non-labeling nature and the ability to detect many chemical species simultaneously. Although bio-Raman data is rich in information, it is considered one of the most complicated and chaotic databases. This is often attributed to its generally large size and the coexistence of Raman active biomolecules in live cells leading to the overlapping of Raman signals. In this regard, direct analysis of bio-Raman data is often difficult and challenging for researchers.

Advanced analytical methods are frequently used to solve the difficulty associated with the application of bio-Raman data in research activities. In particular, non-negative matrix factorization (NMF) is commonly used to disentangle large-sized and complicated spectral data. Unlike other analytical methods, NMF can estimate the factorized spectral components that are very close to the chemical and physical meanings because of its non-negative feature. Running NMF requires knowing the number of the components involved, their initial setting values and scaling factors. One major limitation of NMF is that it does not provide unique composition as per the initial settings. Instead, it provides several possibilities by returning non-negative spectral components close to the truths. Additionally, the possibilities of the spectral components provided by NMF have not been explored in detail. Clarifying the possible ranges will contribute to the more quantitative bio-Raman analysis.

On this account, researchers from Tohoku University: Mr. Hua Yu, Mr. Ziteng Wang, Mr. Mana Nemoto and Professor Shin-ichi Morita in collaboration with Dr. Kazuyuki Suzuta and Mr. Len Ito from R&D Department at Milbon graphically visualized and interpreted the possible ranges given by NMF. Their main objective was to provide a better understanding of the NMF mechanism in a binary component system to widen the scope of bio-Raman research. The binary component system was assumed to overcome the visualization and interpretation complexity. Their research is currently published in the journal, Applied Physics Express.

The authors findings revealed three key relations for the binary component system. First, for the optimized spectral components, the angle between the outlines of the possible ranges given by the NMF will always be smaller than the right angle. Second, the project data points and the regions of the optimized spectral components did not overlap in any way. Third, in the event that the broader band and smaller band are completely overlapped, the vector range corresponding to the smaller band became narrow, almost appearing to be a single vector. Furthermore, the researchers confirmed that the observed relationships are applicable to multi-component systems because the hyperspace vectors exhibit possible ranges equivalent to the dimensions of the component system.

In summary, the research team visualized the NMF analysis process for the binary component system to clarify arbitrariness in NMF. The findings provided more clarifications on the underlying mechanism of NMF. The authors concluded that considering the alternative property between the one-dimensional property of the signals and the complementary vector spaces is critical for achieving NMF in a more comprehensive and meaningful manner. It helps solve the complicated situations associated with the practical application of NMF. In a statement to Advances in Engineering, Corresponding and lead author, Dr. Shin-ichi Morita explained that the study will open new viewpoints, including the realization of more quantitative bio-Raman research.