Multivariate curve resolution combined with estimation by cosine similarity mapping of analytical data.

We developed a multivariate curve resolution (MCR) calculation combined with the mapping of cosine similarity (cos-s) for estimating multiple mixture spectra of chemicals. The cos-s map was obtained by calculating the similarities of the variation of the signal intensities at each scanning parameter, such as the wavelength. The cos-s map was utilized for the initial estimation of the spectra of pure chemicals and also for the restriction of the iterative least-squares calculation of the MCR. These calculations were performed without arbitrary parameters by introducing soft clustering to the cos-s map. The chemically meaningful initial estimation could prevent the convergence at an incorrect local minimum, which frequently happens for the wrong initial estimation of spectra far away from the real answer. Herein, we demonstrated the robustness of this calculation method by applying it for UV/Vis spectra and XRD patterns of multiple unknown chemical mixtures, whose shapes were totally different (broad overlapped peaks and multiple complicated peaks). Pure spectra/patterns were recovered as >84% consistency with the reference spectra, and <6% accuracy of the concentration ratios was demonstrated.