Graph Based Approach for Galaxy Filament Extraction

We propose an original density estimator built from a cloud of points \( \mathcal {X}^{}_{ } \subset \mathbb R ^d\) . To do this, we consider geometric graphs \(\mathcal {G}(\mathcal {X}^{}_{ }, \ r)\) on the cloud. These graphs depend on a radius r. By varying the radius, we see the emergence of large components around certain critical radii, which is the phenomenon of continuum percolation. Percolation allows us to have both a local view of the data (through local constraints on the radius r) and a global one (the emergence of macro-structures). With this tool, we address the problem of galaxy filament extraction. The density estimator gives us a relevant graph on galaxies. With an algorithm sharing the ideas of the Fréchet mean, we extract a subgraph from this graph, the galaxy filaments.