  The development of the phase-imaging ion-cyclotron resonance (PI-ICR)
technique for use in Penning trap mass spectrometry (PTMS) increased the speed
and precision with which PTMS experiments can be carried out. In PI-ICR, data
sets of the locations of individual ion hits on a detector are created showing
how ions cluster together into spots according to their cyclotron frequency.
Ideal data sets would consist of a single, 2D-spherical spot with no other
noise, but in practice data sets typically contain multiple spots,
non-spherical spots, or significant noise, all of which can make determining
the locations of spot centers non-trivial. A method for assigning groups of
ions to their respective spots and determining the spot centers is therefore
essential for further improving precision and confidence in PI-ICR experiments.
We present the class of Gaussian mixture model (GMM) clustering algorithms as
an optimal solution. We show that on simulated PI-ICR data, several types of
GMM clustering algorithms perform better than other clustering algorithms over
a variety of typical scenarios encountered in PI-ICR. The mass spectra of
$^{163}\text{Gd}$, $^{163m}\text{Gd}$, $^{162}\text{Tb}$, and
$^{162m}\text{Tb}$ measured using PI-ICR at the Canadian Penning trap mass
spectrometer were checked using GMMs, producing results that were in close
agreement with the previously published values.
