Statistical approach to determining the cut-off value in the algorithms of substance identification in Fourier transform infrared spectroscopy

Abstract

Abstract The purpose of the paper was to find the approach to determining the cut-off value in the spectral library matching identification algorithm. We used Pearson correlation coefficient as a similarity measure between the spectra, and according to its value between the reference spectra we divided the spectral library into classes. We considered a situation when one of the investigated spectra had an additive narrowband white noise component with a Gaussian distribution. We examined the impact of the cut-off value on the possibility of calculating the probability of right identification in a single identification experiment by means of probability distribution function, when the signal-to-noise ratio is known a priori. The signal-to-noise ratio was taken from the value area where analytical expressions were unknown. In the research we applied numerical methods. The algorithm of determining the cut-off value based on the fundamental principles of the ROC-curves analysis was proposed. The cut-off value was obtained where possible, and the situation for every class was analysed. Maximal probabilities of right identification were obtained.