Multi-class classification of Fermi-LAT sources with hierarchical class definition

In the paper we develop multi-class classification of Fermi-LAT gamma-ray sources using machine learning with hierarchical determination classes. One main challenges in is that size some classes relatively small, for example less than 10 associated belonging to a class. propose structure This enables us have control over and compare performance different numbers particular, class probabilities two-class case can be computed either directly by or summing children classification. We find classifications few large comparable many smaller Thus, on one hand, few-class recovered more while, other gives detailed information about physical nature sources. As result this work, construct three probabilistic catalogs. Two catalogs are based Gaussian mixture model groups classes: requirement minimal number group larger 100, which results six final classes, while has 15, nine The third catalog random forest (abridged)