Masserstein: Linear regression of mass spectra by optimal transport

The linear regression of mass spectra is a computational problem defined as fitting a linear combination of reference spectra to an experimental one. It is typically used to estimate the relative quantities of selected ions. In this work, we study this problem in an abstract setting to develop new approaches applicable to a diverse range of experiments.

To overcome the sensitivity of the ordinary least-squares regression to measurement inaccuracies, we base our methods on a non-conventional spectral dissimilarity measure, known as the Wasserstein or the Earth Mover's distance. This distance is based on the notion of the cost of transporting signal between mass spectra, which renders it naturally robust to measurement inaccuracies in the mass domain.

Using a data set of 200 mass spectra, we show that our approach is capable of estimating ion proportions accurately without extensive preprocessing of spectra required by other methods. The conclusions are further substantiated using data sets simulated in a way that mimics most of the measurement inaccuracies occurring in real experiments.

We have developed a linear regression algorithm based on the notion of the cost of transporting signal between spectra. Our implementation is available in a Python 3 package called masserstein, which is freely available at https://github.com/mciach/masserstein.