Cosmic Web Reconstruction through Density Ridges: Catalogue
  We construct a catalogue for filaments using a novel approach called SCMS
(subspace constrained mean shift; Ozertem & Erdogmus 2011; Chen et al. 2015).
SCMS is a gradient-based method that detects filaments through density ridges
(smooth curves tracing high-density regions). A great advantage of SCMS is its
uncertainty measure, which allows an evaluation of the errors for the detected
filaments. To detect filaments, we use data from the Sloan Digital Sky Survey,
which consist of three galaxy samples: the NYU main galaxy sample (MGS), the
LOWZ sample and the CMASS sample. Each of the three dataset covers different
redshift regions so that the combined sample allows detection of filaments up
to z = 0.7. Our filament catalogue consists of a sequence of two-dimensional
filament maps at different redshifts that provide several useful statistics on
the evolution cosmic web. To construct the maps, we select spectroscopically
confirmed galaxies within 0.050 < z < 0.700 and partition them into 130 bins.
For each bin, we ignore the redshift, treating the galaxy observations as a 2-D
data and detect filaments using SCMS. The filament catalogue consists of 130
individual 2-D filament maps, and each map comprises points on the detected
filaments that describe the filamentary structures at a particular redshift. We
also apply our filament catalogue to investigate galaxy luminosity and its
relation with distance to filament. Using a volume-limited sample, we find
strong evidence (6.1$\sigma$ - 12.3$\sigma$) that galaxies close to filaments
are generally brighter than those at significant distance from filaments.
