SCONCE-SCMS detects cosmic web structures, primarily cosmic filaments and the associated cosmic nodes, from a collection of discrete observations with the extended subspace constrained mean shift (SCMS) algorithms on the unit (hyper)sphere (in most cases, the 2D (RA,DEC) celestial sphere), and the directional-linear products space (most commonly, the 3D (RA,DEC,redshift) light cone).

The subspace constrained mean shift (SCMS) algorithm is a gradient ascent typed method dealing with the estimation of local principal curves, more widely known as density ridges. The one-dimensional density ridge traces over the curves where observational data are highly concentrated and thus serves as a natural model for cosmic filaments in our Universe. Modeling cosmic filaments as density ridges enables efficient estimation by the kernel density estimator (KDE) and the subsequent SCMS algorithm in a statistically consistent way. While the standard SCMS algorithm can identify the density ridges in any "flat" Euclidean space, it exhibits large bias in estimating the density ridges on the data space with a non-linear curvature. The extended SCMS algorithms used in SCONCE-SCMS are adaptive to the spherical and conic geometries and resolve the estimation bias of the standard SCMS algorithm on a 2D (RA,DEC) celestial sphere or 3D (RA,DEC,redshift) light cone.