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
socalled training set method known as
Gaussian process (GP) regression.
Previously, because
of a linearalgebraic 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
fullspectrum 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 linearalgebraic
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 2627, 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 2627, 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
NASAAmes 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
DataII."
CAMCOS Report, June 2007. NASA technical report.


