Comparing similar spectra: From similarity index to spectral contrast angle

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Abstract
We investigated a spectral-contrast-angle (theta) method to determine whether mass spectra of structural isomers are the same or significantly different. This method represents collisionally activated dissociation (CAD) spectra as vectors in space. Mass spectra of different isomers are represented as different vectors, having characteristic lengths and direction. The derived spectral contrast angle, which is a measure of the angle between two vectors corresponding to two closely related spectra, is a measure of whether the mass spectra are the same or significantly different. We compare this method with the similarity index (SI) method and show that the spectral contrast angle method is superior and can differentiate between very similar spectra in cases where the SI cannot. Both methods can be implemented simply in situations where the analyst is called on to decide, on the basis of mass or product-ion spectra, whether reference and unknown compounds are the same or to evaluate the reproducibility of spectra comprised of many peaks.