| Abstract: |
The two-point correlation function (2PCF) of galaxies bears great amounts of information about the large-scale structure (LSS) of the Universe. Galaxy distributions are generally subject to selection effects from anisotropic systematics, thus presenting a ``variable depth'' which, if not estimated properly, will cause bias in the 2PCF, especially for faint galaxy samples. In this talk, I will introduce a machine-learning-based method to recover the "organized randoms" to mitigate the bias in 2PCF caused by variable depth. The basic idea is to find the systematics-induced clustering of galaxies in systematics space by a combination of self-organising maps (SOM) and hierarchical clustering (HC). The grouped galaxies are then re-distribute to the sky, thus yielding the OR. We validate the ``SOM+HC'' method with mock galaxies generated by the Generator of Large-Scale Structure (GLASS). We use a ``data-driven systematics'' test to validate the method against real data. By running the SOM+HC on the mock data with realistic systematics distribution and isotropic selections, we find that the OR recovered from the SOM+HC method can correct a $\sim 3000\sigma$-level of variable-depth-induced bias in the 2PCF to $\sim0.01\sigma$. We also find the proper setup of the SOM+HC to be applied to the real KiDS-Legacy measurement. This method will be used in the $6\time2$-pt analysis with the KiDS-Legacy data, and will also be useful in future LSS surveys including {\textit{Euclid}} and the Legacy Survey of Space and Time (LSST).
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