Multiscale probability mapping: groups, clusters and an algorithmic
  search for filaments in SDSS
  We have developed a multiscale structure identification algorithm for the
detection of overdensities in galaxy data that identifies structures having
radii within a user-defined range. Our "multiscale probability mapping"
technique combines density estimation with a shape statistic to identify local
peaks in the density field. This technique takes advantage of a user-defined
range of scale sizes, which are used in constructing a coarse-grained map of
the underlying fine-grained galaxy distribution, from which overdense
structures are then identified. In this study we have compiled a catalogue of
groups and clusters at 0.025 < z < 0.24 based on the Sloan Digital Sky Survey,
Data Release 7, quantifying their significance and comparing with other
catalogues. Most measured velocity dispersions for these structures lie between
50 and 400 km/s. A clear trend of increasing velocity dispersion with radius
from 0.2 to 1 Mpc/h is detected, confirming the lack of a sharp division
between groups and clusters. A method for quantifying elongation is also
developed to measure the elongation of group and cluster environments. By using
our group and cluster catalogue as a coarse-grained representation of the
galaxy distribution for structure sizes of <~ 1 Mpc/h, we identify 53 filaments
(from an algorithmically-derived set of 100 candidates) as elongated unions of
groups and clusters at 0.025 < z < 0.13. These filaments have morphologies that
are consistent with previous samples studied.
