From SINGS (Spitzer Infrared Nearby Galaxies Survey): Isn’t it a beautiful Hubble tuning fork?

As a first year graduate student of statistics, because of the rumor that Prof. C.R.Rao won’t teach any more and because of his fame, the most famous statistician alive, I enrolled his “multivariate analysis” class without thinking much. Everything is smooth and easy for him and he has incredible memories of equations and proofs. However, I only grasped intuitive concepts like why the method works, not details of mathematics, theorems, and their proofs. Instantly, I began to think how methods can be applied to astronomical data. After a few lessons, I desperately wanted to try out multivariate analysis methods to classify galactic morphology.

The dream died shortly because there’s no data set that can be properly fed into statistical methods for classification. I spent quite time on searching some astronomical data bases including ADS. This was before SDSS or VizieR become popular as now. Then, I thought about applying them to classify supernovae because understanding the pattern of their light curves tells a lot of the history of our universe (Type Ia SNe are standard candle) and because I know some publicly available SN light curves. Immediately, I realize that individual light curves are biased from the sampling perspective. I do not know how to correct them for multivariate analysis. I also thought about applying multivariate analysis methods to stellar spectral types and stars of different mechanical systems (single, binary, association, etc). I thought about how to apply newly learned methods to every astronomical objects that I learned, from sunspots to AGNs.

Regardless of target objects to be scrutinized under this fascinating subject “multivariate analysis,” two factors kept discouraged me: one was that I didn’t have enough training to develop new statistical models in a couple of weeks to reflect unique statistical challenges embedded in data that have missings, irregularities, non-iid, outliers and others that are hardly transcribed into statistical setting, and the other, which was more critical, was that no accessible astronomical database repository for statistical learning. Without deep knowledge in astronomy and trained skills to handle astronomical data, catalogs are generally useless. Those catalogs and data sets in archives are different from data sets from data repositories in machine learning (these data sets are intuitive).

Astronomers would think analyzing toy/mock data sets is not scientific because it’s not leading to any new discovery which they always make. From data analyst viewpoints, scientific advances mean finding tools that summarize data in an optimal manner. As I demanded in Astroinformatics, methods for retrieving information can be attempted and validated with well understood, astrophysically devastated data sets. Pythagoras theorem was proved not only once but there are 39 different ways to prove it.

Seeing this nice poster image (the full resolution image of 56MB is available from the link), brought me some memory of my enthusiasm of applying statistical learning methods for better knowledge discovery. As you can see there are so many different types of galaxies and often times there is no clear boundary between them – consider classifying blurry galaxies by eyes: a spiral can be classified as a irregular, for example. Although I wish for automatic classification of these astrophysical objects, because of difficulties in composing a training set for classification or collecting data of distinctive manifold groups for clustering, as much as complexity that this tuning fork shows, machine learning procedures is equally complicated to be developed. Complex topology of astronomical objects seems to be the primary reason of lacking in statistical learning applications compared to other fields.

Nonetheless, multivariable analysis can be useful for viewing relations from different perspectives, apart from known physics models. It may help to develop more fine tuned physics model by taking latent variables into account that are found from statistical learning processes. Such attempts, I believe, can assist astronomers to design telescopes and to invent efficient ways to collect/analyze data by knowing which features are more significant than others to understand morphological shape of galaxies, patterns in light curves, spectral types, etc. When such experiences accumulate, different insights of physics can kick in like scientists scrambled and assembled galaxies into a tuning fork that led developing various evolution models.

To make a long story short, you have two choices: one, just enjoy these beautiful pictures and apprehend the complexity of our universe, or two, this picture of Hubble’s tuning fork can be inspirational to you for advances in astroinformatics. Whichever path you choose, it’s your time worthy.

The sixth data release of the Sloan Digital Sky Survey (SDSS DR6) is available at http://www.sdss.org/dr6. Additionally, Catalog Archive Service (CAS) and
SQL interface to access the catalog would be useful to data searching statisticians. Simple SQL commends, which are well documented, could narrow down the size of data and the spatial coverage.

Part of my dissertation was about creating nonparametric multivariate analysis tools with convex hull peeling and I used SDSS DR4 to apply those convex hull peeling tools to explore celestial objects in the multidimensional color space without projections (dimension reduction). SDSS CAS might fulfill the needs of those who are looking for data sets to conduct

• massive multivariate data analysis,
• streaming data analysis (strictly, SDSS is not streaming but the data base is updated yearly by adding new observations and depending on memory, streaming data analysis can be easily simulated) and
• application of his/her new machine learning and statistical multivariate analysis tools for new discoveries.

Particularly, thanks to whole northern hemisphere survey, interesting spatial statistics can be developed such as voronoi tessellation for spatial density estimation. It also provides a vast image reservoir as well as the catalog of massive multivariate spatial data.

Oh, by the way, the paper discusses changes and improvement in the recent data release. The SDSS DR6 includes the complete imaging of the Northern Galactic Cap and contains images and parameters of 287 million objects over 9583 deg^2, and 1.27 million spectra over 7425 deg^2. The photometric calibration has improved with uncertainties of 1% in g,r,i and 2% in u, significantly better than previous data releases. The method of spectrophotometric calibration has changed and resulted 0.35 mags brighter in the spectrophotometric scale. Two independent codes for spectral classifications and redshifts are available as well.