  Compact stellar systems such as Ultra-compact dwarfs (UCDs) and Globular
Clusters (GCs) around galaxies are known to be the tracers of the merger events
that have been forming these galaxies. Therefore, identifying such systems
allows to study galaxies mass assembly, formation and evolution. However, in
the lack of spectroscopic information detecting UCDs/GCs using imaging data is
very uncertain. Here, we aim to train a machine learning model to separate
these objects from the foreground stars and background galaxies using the
multi-wavelength imaging data of the Fornax galaxy cluster in 6 filters, namely
u, g, r, i, J and Ks. The classes of objects are highly imbalanced which is
problematic for many automatic classification techniques. Hence, we employ
Synthetic Minority Over-sampling to handle the imbalance of the training data.
Then, we compare two classifiers, namely Localized Generalized Matrix Learning
Vector Quantization (LGMLVQ) and Random Forest (RF). Both methods are able to
identify UCDs/GCs with a precision and a recall of >93 percent and provide
relevances that reflect the importance of each feature dimension %(colors and
angular sizes) for the classification. Both methods detect angular sizes as
important markers for this classification problem. While it is astronomical
expectation that color indices of u-i and i-Ks are the most important colors,
our analysis shows that colors such as g-r are more informative, potentially
because of higher signal-to-noise ratio. Besides the excellent performance the
LGMLVQ method allows further interpretability by providing the feature
importance for each individual class, class-wise representative samples and the
possibility for non-linear visualization of the data as demonstrated in this
contribution. We conclude that employing machine learning techniques to
identify UCDs/GCs can lead to promising results.
