CAMCOS Project

Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data
2006-2007

SJSU CAMCOS Logo
Sponsor: NASA Ames Research Center
Liaisons: Dr. Paul Gazis, Dr. Tim Lee, Dr. Ashok Srivastava, and Dr. Michael Way
Supervisors: Dr. Bem Cayco, Dr. Leslie Foster, and Dr. Wasin So
Fall 2006 Improved linear algebra methods for redshift computation from limited spectrum data
Supervisors Dr. Bem Cayco, Dr. Wasin So
Team Leaders Maheen Khan, Genti Zaimi, and David Shao
Student Team Miranda Braselton, Miguel Rodriguez, Jason Smith, Kelley Cartwright, Michael Hurley, Jimmy Ying
Abstract

The redshift of a galaxy allows us to measure the rate at which it is moving away from us by analyzing the spectrum of the light it emits. Recently, Drs. Way and Srivastava have studied novel methods in recovering the redshift of a galaxy from photometric data representing a greatly reduced amount of information about its spectrum. One of these methods is a so-called training set method known as Gaussian process (GP) regression.

Previously, because of a linear-algebraic bottleneck in the GP regression algorithm, only small training sets (e.g., 1000 points) could be used. In this presentation, we discuss several improved linear algebra methods that allow GP regression to be extended to much larger training sets (e.g., 180,000 points). We find that the performance of GP regression improves as the size of the training set increases. However, we also find that GP does not actually perform better than simpler regression methods when bigger training sets are used.


CAMCOS
Presentation
San Jose, CA. Friday, December 8, 2006. Slides.
CAMCOS
Report
January, 2007.
Spring 2007 Improved linear algebra methods for redshift computation from limited spectrum data II
Supervisor Dr. Les Foster
Team Leaders Alex Waagen
Student Team Nabeela Aijaz, Michael Hurley, Apolo Luis, Joel Rinsky, Chandrika Satyavolu
Abstract

The redshift of a galaxy allows us to measure the rate at which it is moving away from us by analyzing the spectrum of the light it emits. Astronomers from NASA and elsewhere often have broadband measurements of the light from a galaxy but do not have direct full-spectrum measurements of the redshift of this light. Therefore, it is useful to be able to predict the redshift given only these broadband measurements.

One approach that can be used to do this is the Gaussian process technique, a method in the general area of machine learning. However, the traditional Gaussian process approach requires solving large systems of linear equations, and in practice, the systems of equations can be so large (e.g.,180, 000 × 180, 000) that it is impossible to solve the equations exactly in a reasonable amount of time. We discuss approximate solutions to the system of equations using low rank matrix approximations. We obtain methods that are fast, accurate, numerically stable, and quite general; in fact, our methods essentially completely remove the linear-algebraic bottleneck from the Gaussian process approach.


CAMCOS
Presentation
San Jose, CA. Wednesday, May 16, 2007. Slides.
CAMCOS
Report
June, 2007. Reprint.
Related Activity
 
Presentations
  • Foster, L., "Application of Stable and Efficient Gaussian Process Calculations to Dynamical System Prognostics," NASA’s Aviation Safety Technical Conference, St. Louis, MO, October, 2007.  Invited Talk. Joint work with Ashok Srivastava and Santanu Das.

  • Foster, L., "Stable and Efficient Gaussian Process Calculations," NASA’s Data Mining in Aeronautics, Science, and Exploration Systems Conference (DMASES 2007 http://ti.arc.nasa.gov/projects/dmases/2007/index.php ), Mountain View, CA, June 26-27, 2007. Invited Talk. Slides.

  • Waagen, A. "Approximating Redshifts with the V Formulation Method", ” NASA’s Data Mining in Aeronautics, Science, and Exploration Systems Conference (DMASES 2007 http://ti.arc.nasa.gov/projects/dmases/2007/index.php), Mountain View, CA, June 26-27, 2007. Poster Session.

  • Braselton, M., "Improved Linear Algebra Techniques for Photometric Redshift Calculation," Northern California Undergraduate Mathematics Conference, Sonoma State University, Rhonert Park, CA, April 21, 2007.

Publications
  • L. Foster, A. Waagen, N. Aijaz, M. Hurley, A. Luis, J. Rinsky, C. Satyavolu, P. Gazis, A. Srivastava, and M. Way. "Stable and Efficient Gaussian Process Calculations." Accepted to the Journal of Machine Learning Research, 2009.

  • L. Foster, A. Waagen, N. Aijaz, A. Luis, and J. Rinsky. Presentation at Division seminar at NASA-Ames Research Center, Mountain View, CA, June 20, 2007.

  • L. Foster, A. Waagen, N. Aijaz, M. Hurley, A. Luis, J. Rinsky, and C. Satyavolu. "Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data-II." CAMCOS Report, June 2007. NASA technical report.



Center for Applied Mathematics, Computation and Statistics
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