The results on this page are described in more detail in Ball et al. (2004) (astro-ph/0306390). The catalogue containing the assigned types is here.
Artificial neural networks were used to predict Hubble types, spectroscopic types, and photometric redshifts galaxies. We showed that the Hubble type can be predicted from SDSS data to the same accuracy as that assigned by human experts. The main results are discussed below, with a further page here giving more details and plots than the paper, since a similar discussion has not been given elsewhere.
Dataset
The training sets were from the SDSS Data Release One (DR1), matched to the galaxies for which the types have been assigned. There is a paper describing DR1, which extends the paper describing the Early Data Release.
Galaxy parameters
The following parameters, available from DR1, were used. Further details are in the paper or in the SDSS SkyServer Schema browser.
1 Petrosian radius in r band
2 50 percent light radius in r (r_50)
3 90 percent light radius in r (r_90)
4 de Vaucouleurs profile radius in r
5 Exponential profile radius in r
6 de Vaucouleurs profile axial ratio in r
7 Exponential profile axial ratio in r
8 log likelihood of de Vaucouleurs galaxy light profile
9 log likelihood of exponential profile
10 galaxy surface brightness
11 concentration index r_50/r_90 in r
12-15 model u-g, g-r, r-i, i-z colours
16-19 Petrosian u-g, g-r, r-i, i-z colours
20-24 model u g r i z magnitudes
25-29 Petrosian u g r i z magnitudes
Morphological Type
The eyeball morphological type can be predicted with a correlation of 0.93 and rms of 0.55. The range is 0 to 6 (elliptical to spiral).
Network type versus morphological type. Note that the the targets, assigned by human experts are to the nearest 0.5 in type.
An automated measure of morphological type developed for the SDSS, known as TP[auto], which requires galaxy images of 25+ pixels in size, can also be predicted with 0.90 correlation.
Spectral Type
The networks are able to predict the eClass spectral type with a correlation of 0.95 and rms deviation of network type from target type of 0.06. The range of targets is approximately -1 (spiral galaxies) to 0.5 (elliptical).
Network type versus eClass
This is using the parameter set 1 to 29. No subset of parameters performs as well, although some are close, e.g. the four model colours give 0.94.
Photometric Redshifts
In principle any parameter describing the galaxies could be predicted if it is available in the training set, for example redshift. Other groups also studied this (e.g. Firth et al 2003, Tagliaferri et al 2002) and achieved comparable results.
Network redshift versus redshift. Some large scale structure is seen as vertical banding in the target redshifts.
General Neural Network Issues
There are numerous issues with the use of neural nets to perform these sorts of predictions. The nature of the neural nets is that you could be doing something wrong and they will still give reasonable, but not quite so good, results. Some of the PhD work involved making sure this is avoided by exploring the issues so that confidence is gained in the predicted galaxy types.
Training algorithm: previous work in astronomy has used either standard gradient descent backpropagation or the quasi-newton method. However in much neural net research the Levenberg-Marquardt algorithm has been found to be the fastest to converge for networks up to a few hundred weights. It is a combination of gradient descent, which rapidly descends steep gradients in the error space, and quasi-Newton, which is more accurate around the minimum, although it only works for a single output, so e.g. quasi-newton is still needed if multiple outputs are used, i.e. for classification as opposed to regression.
Effect of architecture: the number of hidden neurons has little effect beyond 4:1. Here 8:1 nets are quoted. The networks are better than the single neuron, a linear classifier, e.g. 0.94 correlation and 0.062 rms as opposed to 0.89 and 0.084 for eClass. Also, the residuals (network type - target type) are a much stronger function of target type for the single neuron - the net type versus target type plot is still a curve rather than a straight line.
Further aspects of the neural nets, including many plots and details not mentioned in the paper are here.