When investigating astronomical objects, like active galactic nuclei (AGN), astronomers compare data about those objects from different telescopes at different wavelengths. This requires positional cross-matching to find the closest counterpart within a given radius on the sky.
- AT20G Bright Source Sample (BSS) catalogue : 320 objects, listing the brightest sources from the AT20G radio survey
- SuperCOSMOS all-sky galaxy catalogue. : 240 million objects, listing galaxies observed by visible light surveys
Positions of stars and galaxies is usually recorded in either equitorial or Galactic coordinates.
A point on the celestial sphere is given by two coordinates:
- Right ascension: The angle from the vernal equinox to the point, going East along celestial equator;
- Declination: The angle from the celestial equator to the point, going North (negative for South)
To calculate the redshift of a distant galaxy, the most accurate method is to observe the optical emission lines and measure the shift in wavelength. However, this process can be time consuming and is thus infeasible for large samples.
For many galaxies we simply don't have spectroscopic observations.
Instead, we can calculate the redshift by measuring the flux using a number of different filters and comparing this to models of what we expect galaxies to look like at different redshifts.
We will use machine learning to obtain photometric redshifts for a large sample of galaxies. We will use the colour indices (u-g, g-i, r-i and i-z) as our input and a subset of sources with spectroscopic redshifts as the training dataset.
Decision trees are a tool that can be used for both classification and regression. In this module we will look at regression, however, in the next module we will see how they can be used as classifiers.
Decision trees map a set of input features to their corresponding output targets. This is done through a series of individual decisions where each decision represents a node (or branching) of the tree.
In decision tree regression, the possible outputs are a finite set of values that correspond to the number of leaves/end points in the tree. Ideally we want as many points as possible to give a good approximation of the 'continuous' parameter space, whilst avoiding overfitting.
In classification, the predictions are from a fixed set of classes, whereas in regression the prediction typically corresponds to a continuum of possible values.
In regression, we measure accuracy by looking at the size of the differences between the predicted values and the actual values. In contrast, in classification problems a prediction can either be correct or incorrect. This makes measuring the accuracy of our model a lot simpler.
In terms of implementation using decision trees, there is very little difference between classification and regression. The only notable difference is that our targets are classes rather than real values. When calculating the accuracy, we check whether the predicted class matches as the actual class.
The galaxy zoo universe catalogue we are using is a sample of galaxies where at least 20 human classifiers (such as yourself) have come to a consensus on the galaxy type.
The features that we will be using to do our galaxy classification are colour index, adaptive moments, eccentricities and concentrations. These features are provided as part of the SDSS catalogue. Colour indices are the same colours (u-g, g-r, r-i, and i-z) we used for regression. Studies of galaxy evolution tell us that spiral galaxies have younger star populations and therefore are 'bluer' (brighter at lower wavelengths). Elliptical galaxies have an older star population and are brighter at higher wavelengths ('redder'). Eccentricity approximates the shape of the galaxy by fitting an ellipse to its profile. Eccentricity is the ratio of the two axis (semi-major and semi-minor). The De Vaucouleurs model was used to attain these two axis. To simplify our experiments, we will use the median eccentricity across the 5 filters. *Adaptive moments also describe the shape of a galaxy. They are used in image analysis to detect similar objects at different sizes and orientations. We use the fourth moment here for each band. Concentration is similar to the luminosity profile of the galaxy, which measures what proportion of a galaxy's total light is emitted within what radius. A simplified way to represent this is to take the ratio of the radii containing 50% and 90% of the Petrosian flux. The Petrosian method allows us to compare the radial profiles of galaxies at different distances.