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PS reprint
Coryn A. L. Jones
Institute of Astronomy, Madingley Road, Cambridge, United Kingdom
Mike Irwin
Royal Greenwich Observatory, Madingley Road, Cambridge, United Kingdom
Ted von Hippel
WIYN Telescope, National Optical Astronomy Observatories, Tucson, AZ
Traditional methods of stellar classification are slow and arguably subjective. A robust, automated method is an essential requirement if stellar classification is to continue to be an important tool in the face of increasingly large data acquisition rates. We have been investigating the use of Artificial Neural Networks (ANNs) with a Principal Components Analysis (PCA) front-end compression as a means of quantifying stellar spectral classification.
We have scanned and reduced some 100 IIaO plates taken as part of the
Michigan Spectral Survey (Houk 1984). This has provided a set of some
15000 spectra down to 
with a spectral coverage of 
at a two pixel resolution of about 
. This
corresponds to 820 flux bins per spectrum. Of these, we have selected
5000 high quality spectra across all spectral types which have 2D
classifications from Houk & Smith-Moore (1988) (and earlier
volumes). These classifications are used as the ``targets'' to train
our neural networks.
Figure 1: A: Variance of data explained by most significant eigenvectors. B: ANN error as a function of eigenvector representation of spectra.
Figure 1a: PS 24 Kb, Figure 1b: PS 26 Kb
Our principal classification tool is a neural network architecture known as a Back Propagation Neural Network (see, e.g., von Hippel et al.\ 1994; Jones et al. 1996). The neural network consists of a number of weights which connect the inputs (the spectrum), to the outputs (the classification parameters). Training the network performs a non-linear mapping of the spectra onto the classification space and sets the network weights. This process can be considered as a minimization in an N-dimensional space, where N is the number of resolution elements in the spectrum. The network is trained using half of our data. The performance of the network is evaluated by using it to classify the other half of the data set, and comparing these classifications with the original catalogue classifications.
In terms of classification, a spectrum contains redundant information. Thus we can increase the network training speed and over-determination factor by compressing the data. It can be shown that a set of N-dimensional spectra are optimally represented in a linear fashion by a set of basis vectors which are the eigenvectors of the covariance matrix of the spectra (Storrie-Lombardi et al. 1994). Furthermore, the eigenvalues are proportional to the variance explained by each eigenvector, so we can sort the eigenvectors into a significance order. Figure 1a shows that just the first 50 eigenvectors reproduce over 96% of the variance in the data. While we do not use the eigenvectors directly to classify the data (the spectral classification problem is not linearly separable), it can be informative to analyze the components. Figure 2 shows the first 10 eigenvectors. Note that the continuum shape is spread over many components, as are the major lines of Ca H+K and the Hydrogen Balmer lines. Note also, that component 7 strongly represents the M stars on account of the strong TiO features.
In order to investigate the effect of the number of eigenvectors used on the classification error, we trained a M:5:1 network to classify spectral types only. Figure 1b shows the classification error for a spectral representation using M eigenvectors, for M in the range 1--50. We see that using more than 25 eigenvectors is probably not necessary for the spectral type problem. Higher eigenvectors are presumably adding noise as fast as they are adding spectral information.
Figure 2: First 10 normalised eigenvectors, plotted on the same scale. The sign of features is arbitrary.
Figure 2: PS 164 Kb
Using the first 50 principal components rather than the whole 820 flux bins as the ANN input yields a data compression factor of about 16. This number of components was used to develop a 50:5:2 network to simultaneously classify spectra into luminosity classes (III, IV or V) and the full range of spectral types. The results are shown in Figure 3. We attempted classification with line only and line+continuum spectra. Despite potential inter-plate emulsion variations and reddening effects, the line+continuum classifications were of superior quality.
Figure 3: ANN classification results. The left column is for
line + continuum spectra and the right for line only.
The spectral type (SpT) is coded onto a 1--57 range.
Figure 3: PS 396 Kb
CALJ would like to thank the ADASS Conference organizers for their generous support in enabling him to attend this conference.
Houk, N., & Smith-Moore 1988, University of Michigan Catalogue of 2D Spectral Types for the HD Stars, Vol. 4, and earlier volumes
Jones, C. A. L., et al. 1996, in preparation Storrie-Lombardi, M. C., et al. 1994, Vistas in Astronomy, 38, 331
von Hippel, T., et al. 1994, MNRAS, 269, 97