Image from Gene Smith's Astonomy Tutorial
The number of parameters describing a galaxy can vary from one to infinity. It is desirable to have as much information as possible about the physical processes involved in the least number of parameters. The smallest number here is of course one, and so the notion of a galaxy `type' is useful. The neural networks are a way of mapping in a general nonlinear way the parameters (e.g. the standard outputs from the Sloan Survey) onto a type.
Measures of type include:
My original motivation for studying this area of astronomy was not neural networks but cosmology and the large scale structure of the universe. In particular the book `Large Scale Structures in the Universe' by Anthony Fairall, purchased at the Federation of Astronomical Societies meeting in Cambridge in 1996 was influential. The tricky part is finding something original to do in the area which is not already being done by other members of the Sloan Survey collaboration. Thus looking at galaxy types and large scale structure, which has been done but can be done in unprecendented detail with the Sloan data, and the use of a method for getting large samples of typed galaxies, sounded interesting. The neural nets are simply one way of doing this.
Typical `cone plot' of galaxy position versus redshift. This is
from the 2dF Galaxy
Redshift Survey rather than the Sloan : ). Note that every galaxy
is treated in the same way, as a dot.
Although originally motivated by models of biological neurons, the
artificial neural networks here are simply a nonlinear statistical
method. The idea is that a set of parameters is mapped onto an output
or outputs by adjusting the weights between the interconnnected neurons
by the use of a training algorithm. The networks used here are in the
common form of one dimensional layers of neurons, each neuron in each
layer being connected to each neuron in adjacent layers but no others.
They are known as `multilayer perceptrons', although the neurons in
fact represent a nonlinear operation on the sum
of their inputs rather than a threshold, which is what a perceptron is.
Schematic artificial neural network (Storrie-Lombardi et al, MNRAS 259 8P)
The most commonly used training algorithm in astronomy has been `backpropagation', where the weights are adjusted according to an algorithm which is propagated back through the network. Here a faster algorithm is used, the Levenberg-Marquardt. In networks with up to a few hundred weights this is thought to be the fastest to converge to a minimum in the `error space'. This is the space of values of the `cost function', a measure of the difference between the network output and the desired type, which is given by a training set in which parameters corresponding to known types are presented in turn to the network. The network is then able to assign types to further sets of parameters of which the training set was representative. The plots in the results pages show how the networks here manage at doing this for target types for galaxies, by plotting the network type against the target type for galaxies which have a target type, but which the network has not seen - a test set.
Last modified: Mon Dec 20 17:18:05 CST 2004