Quarterly Progress Report December 15, 2005

AISRP: NAS5-02098

Novel Approaches to Supervised and Unsupervised Data Exploration

David Bazell, PI

[Summary of Progress]{.underline}

Over the past three months we were able to complete a significant
scientific application of the class discovery method we have been using.
We reported the initial work on this scientific scenario in our previous
quarterly report. Some of the details have changed, which we will cover
here.

The purpose of this scenario was to apply the class discovery technique
to a set of data containing objects from the Sloan Digital Sky Survey
that were classified as "unknown". This means that the SDSS
spectroscopic pipeline could not confidently identify the objects as
belonging to one of the standard classes: stars, galaxies, AGN, or
late-type stars. The spectra of these objects were also examined
visually by a small group of people. If they still could not determine a
confident classification, the objects were assigned to the unknown
class. This makes these unknown objects of potential scientific
interest. Thus, we wanted to apply our technique of class discovery to
see if we could determine subclasses of the unknown class. This would
provide further objective structure to the unknown class.

We created our data set by identifying all unknown objects with a
signal-to-noise ratio of greater than 3 and a redshift less than 2.3.
This produced a set of 1764 unknown objects. We supplemented this data
set with 2000 galaxies, 2000 stars, 2000 AGN and 2000 late-type stars,
resulting in a data set of 9764 objects. Each object was described by
four color indices based on the primary SDSS photometry: u-g, g-r, r-i,
i-z. While our primary goal was to search for substructure in the
unknown class we were also interested in seeing if some of the unknown
objects would be clustered with known objects and if some of the known
objects would be clustered with unknown objects. While we were quite
certain of the classification of the known objects, (galaxies, etc.) we
were quite uncertain of the classification of the unknown objects: were
they really examples of known class objects or were they a new type of
object?

We applied the class discovery technique using the Bayesian Information
Criterion to determine the best set of model parameters. The final model
was a mixture of 16 components (Gaussian probability distributions) that
best described our data set. Of these 16 components, 2 were
"nonpredefined" which means they described clusters of objects that
contained almost no data from known classes. These nonpredefined
components describe independent clusters of data that are essentially
outliers from the rest of the data set.

These two nonpredefined components effectively described subclasses of
the unknown objects. One component was 58% unknown objects while the
other was 91% unknown objects. We looked at the spectra of these objects
to see if we could determine in more detail what types of objects they
were. One component consists of mainly blue, featureless spectra which
we believe are most likely sd0 or DA white dwarfs. The other component
appears to consist mainly of low signal-to-noise G-K stars.

In addition to these subclasses of the unknown class we found that two
other mixture components contained 81% of the galaxies in our data set.
These two components did a very good job of separating the galaxies into
two clusters which coincided with the bimodal color distribution
described recently in the literature (e.g., Strateva, et al. (2001);
Seibert, et al. (2005)), one component describing blue galaxies and the
other describing red galaxies.

We wrote up this work and submitted a paper to the Astrophysical Journal
early in December---Bazell, Miller, and SubbaRao, (2005). Many more
details can be found there.

We are currently looking in more detail at the bimodal color
distribution. We have created a multiwavelength data set extending from
the IR to the visible to the UV using 2MASS, SDSS, and Galex data. We
are in the process of using this dataset to investigate the bimodal
color distribution and to see if we can find a more detailed
subclassification of the data. We will use an unsupervised mixture
modeling approach that clusters the data and plan to compare this with a
k-means clustering approach.

We will be presenting a poster describing this work at the January AAS
meeting in Washington, D.C.

[Problems and Issues]{.underline}

No new problems or issues to report.

[Plans for Next Quarter]{.underline}

Continue work on multiwavelength classification of galaxy data and
bimodal color distribution.

Continue work on clustering with constraints.

[References:]{.underline}

Bazell, D., Miller, D. J., & SubbaRao, M. 2005, ApJ submitted,
astro-ph/0512119

Seibert, M., et al., 2005, ApJ, 619, L23

Strateva, I., et al. 2001, AJ, 122, 1861