Shape-based clustering of synthetic Stokes profiles using k-means and k-Shape

Context. The shapes of Stokes profiles contain a great deal of information about the atmospheric conditions that produced them. However, a variety of different atmospheric structures can produce very similar profiles. Thus, it is important for a proper interpretation of the observations to have a good understanding of how the shapes of Stokes profiles depend on the underlying atmosphere. An excellent tool in this regard is forward modeling, namely, computing and studying synthetic spectra from realistic simulations of the solar atmosphere. Modern simulations routinely produce several hundred thousand spectral profiles per snapshot. With such numbers, it becomes necessary to use automated procedures in order to organize the profiles according to their shape. Here, we illustrate the use of two complementary methods, k-means and k-Shape, to cluster similarly shaped profiles and demonstrate how the resulting clusters can be combined with knowledge of the simulation's atmosphere to interpret spectral shapes.Aims. We aim to showcase the use of clustering analysis for forward modeling. In particular, we wish to introduce the k-Shape clustering method to the solar physics community as a complement to the well-known k-means method.Methods. We generated synthetic Stokes profiles for the Ca II 854.2 nm line using the Multi3D code from a Bifrost simulation snapshot. We then applied the k-means and k-Shape clustering techniques to group the profiles together according to their shape and investigated the within-group correlations of temperature, line-of-sight velocity, and line-of-sight magnetic field strengths.Results. We show and compare the classes of profile shapes we retrieved from applying both k-means and k-Shape to our synthetic intensity spectra. We then show the structure of the underlying atmosphere for two particular classes of profile shapes retrieved by the clustering and demonstrate how this leads to an interpretation for the formation of those profile shapes. We applied both methods to the subset of our profiles containing the strongest Stokes V signals and we demonstrate how k-Shape can be qualitatively better than k-means at retrieving complex profile shapes when using a small number of clusters.