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A filament is a one-dimensional, smooth, connected structure embedded in a multi-dimensional space that characterizes the high density regions. Matter in the Universe tend to aggregate around these filaments which weave our Universe into an intricate network structure. We use ridges of density function (density ridges) as tracers for the filaments and apply our method to the SDSS DR12 to construct a filament catalogue.

This is a joint project of department of Statistics, department of Physics, and the McWilliams center for Cosmology at Carnegie Mellon University. This is also a project of the astrostatistics group at Carnegie Mellon University.

References:

Cosmology--

1. Chen, Yen-Chi, Shirley Ho, Peter E. Freeman, Christopher R. Genovese, and Larry Wasserman. ``Cosmic Web Reconstruction through Density Ridges: Method and Algorithm." arXiv: 1501.05303

2. Chen, Yen-Chi, Shirley Ho, Jon Brinkmann, Peter E. Freeman, Christopher R. Genovese, Donald P. Schneider, and Larry Wasserman. ``Cosmic Web Reconstruction through Density Ridges: Catalogue." arXiv: 1509.06443

3. Chen, Yen-Chi, Shirley Ho, Ananth Tenneti, Rachel Mandelbaum, Rupert Croft, Tiziana DiMatteo, Christopher R. Genovese, and Larry Wasserman. ``Investigating Galaxy-Filament Alignment in Hydrodynamic Simulations using Density Ridges." arXiv: 1508.04149

4. Chen, Yen-Chi, Shirley Ho, Rachel Mandelbaum, Neta Bahcall, Joel Brownstein, Peter E. Freeman, Christopher R. Genovese, Donald P. Schneider, and Larry Wasserman. ``Detecting Effects of Filaments on Galaxy Properties in Sloan Digital Sky Survey III." arXiv: 1509.06376

Statistical Theory--

1. Chen, Yen-Chi, Christopher R. Genovese, and Larry Wasserman. ``Asymptotic Theory for Density Ridges."  The Annals of Statistics 43, no. 5 (2015): 1896-1928. arXiv: 1406.5663

2. Genovese, Christopher R., Marco Perone-Pacifico, Isabella Verdinelli, and Larry Wasserman. ``Nonparametric Ridge Estimation." The Annals of Statistics 42, no. 4 (2014): 1511-1545.

Algorithm--

1. Chen, Yen-Chi, Christopher R. Genovese, Shirley Ho, and Larry Wasserman. ``Optimal Ridge Detection using Coverage Risk." arXiv: 1506.02278

2. Chen, Yen-Chi, Christopher R. Genovese, and Larry Wasserman. ``Generalized Mode and Ridge Estimation." arXiv: 1406.1803

3. Ozertem, Umut, and Deniz Erdogmus. "Locally Defined Principal Curves and Surfaces. " The Journal of Machine Learning Research 12 (2011): 1249-1286.