An initial estimation method using cosine similarity for multivariate curve resolution: application to NMR spectra of chemical mixtures

Multivariate curve resolution (MCR) has been widely utilized to reveal the constituents of chemicals from multiple spectral data of chemical mixtures. In the MCR calculation, the singular value decomposition (SVD) has been utilized to obtain the initial estimation of the spectra for pure chemicals and they are adjusted to obtain the best fit using the alternating least squares (ALS) algorithm. However, wrong initial estimation by SVD frequently leads to convergence at an incorrect local minimum of the least square error. To overcome this problem, we have developed a robust calculation technique, which utilizes a new initial estimation using cosine similarity, and the following optimization was performed by MCR. The calculation was applied for 1H-NMR mixture spectra of 4 different chemicals, and this methodology could recover the spectra of pure chemicals (>85% consistency) and the concentration profile for each mixture within an accuracy of <10%.