This project is a demonstration of how machine learning can be used to automatically classify galaxies observed by the Sloan Digital Sky Survey (SDSS), a long-running astronomical survey that has covered more than a third of the sky, and collected photometric (imaging) data on more than 500 million targets.  A related project, the Galaxy Zoo (http://www.galaxyzoo.org/) is a crowdsourced citizen science project which aims to use volunteers to classify galaxies by type.  Most galaxies fall into a continuum between ellipticals (featureless and ellipsoidal) and spiral galaxies like our own Milky Way; spirals can be further broken down into whether they appear face- or edge-on.  The first year of Galaxy Zoo was able to provide some 60 million votes on 900,000 galaxies in the sample.  As galaxy classification is not an exact science, especially with amateurs, multiple votes are useful in building a reliable set.

These manual classifications thus form a training set which can be used to build a classification model for 4 types of galaxies within the set: ellipticals, mergers, and face- and edge-on spirals.  Here, I have shown how a combination of multinomial logistic regression (softmax) and dimensionality reduction using Principal Component Analysis (PCA) can be used to automate this determination. Rather than using full imaging data, I am simply using the features that the survey extracts programmatically from photometric data, including magnitudes, dust extinction, and parametrized fits to two simple models which are commonly used to fit galactic brightness profiles: de Vaucouleurs and exponential.


Steps:
1) I have collected SDSS data from the survey's SkyServer (http://skyserver.sdss.org/), which provides a SQL interface to photometric and galaxy zoo data.  Because the public limit on data download for the site is 500MB, I have prioritized galaxies receiving the most votes in the Galaxy Zoo project.  A quick estimate tells me that I can download photometric data for the top 85K galaxies, which turns into a lower bound of about 70 votes.  Galaxy Zoo vote data is also available on this server, and I used a SQL join to include these variables in the downloaded table.

2) Working in an iPython notebook with Pandas data frames, I apply cuts to remove high redshift galaxies, as well as any galaxy with non-physical model parameters, such as negative radii.  I then correct all magnitude and flux parameters to account for extinction effects from dust.

3) Applying logistic regression on a parameter set chosen based on correlation with the target output, I find peak accuracy with a feature set size of N=50.  However, this model fails to classify galaxy merger cases, the smallest class within the set.  Resampling to use a more balanced training set allows mergers to be classified, but at a cost of accuracy elsewhere.  Finally, using PCA to select a small set of optimized features prior to regression proves to be the most fruitful path, correctly classifying ~95% of cases.