22 SIMPÓSIO BRASILEIRO DE AUTOMAÇÃO INTELIGENTE CEFET-PR, 13 a 15 de Setembro de 1995 Curitiba Paraná

Automated Spectral Classification Using Neural Networks E. F. Vieira1 and J. D. Ponz2

1 LAEFF 2 ECNOD/ESA Villafranca, P. O. Box 50727, 28080 Madrid, Spain efv@laeff.esa.es, jdp@vilspa.esa.es

Abstract

Along the life of the International Ultraviolet Explorer (IUE) astronomical satellite project, a large archive with spectral data has been generated, requiring automated classification methods to be analyzed in an objective formo Previous automated classification methods used with IUE spectra were based on multivariate statistics. In this paper, we compare three classification methods that can be directly applied to spectra in the archive:

- metric distance, - supervised classification using Artificial Neural Networks (ANN) and - unsupervised classification using Self Organized Maps (SOM).

These methods are used to classify IUE low-dispersion spectra of normal stars with spectral types ranging from 03 to G5. The classification based on supervised artificial neural networks performs better than the metric distance and the current SOM classification, allowing the determination of the spectral classes with an accuracy of 1.1 spectral subclasses. The unsupervised classification can be also use to test the supervised technique.

1. Introduction

This paper explores the application of automated methods to the problem of classification of stellar spectra.

The availability of large spectral archives and the efficiency achieved with modern instrumen­tation require automated classification methods to improve the classification by visual inspection. These methods are still in exploratory phase; the aims are clear, to devise an objective, repeatable and robust classification scheme providing an es­timation of systematic and random errors, and allowing the quantification of spectral resolution and signal to noise ratio on classification errors.

Traditionally, spectra have been classified manually according to star temperatures and lu­minosity classes. In this preliminary work we con­sider temperature as parameter to be classified. The spectral or temperature classes are named O, B, A, F, G, K and M where O is for the hottest stars and M is for the coldest ones. Further sub­divisions of classes (e.g. AO, AI, A2, etc.) is

Send offprint requests to: J. D. Ponz

based on detailed spectral features (Allen 1976). The estimated error in the classification made by human experts is about 0.5 spectral sub classes (Weaver 1994) (von Hippel, Storrie-Lombardi, & Storrie-Lombardi 1994) .

Automated classifiers of stellar spectra can be divided into metric distance algorithms, mul­tivariate statistics and artificial neural networks (hereafter ANN) . Metric distance methods were originally proposed by K urtz and LaSala (K urtz 1982) (Kurtz 1984) (Lasala & Kurtz 1985) and have been used by Penprase (Penprase 1994) to classify stellar spectra using the digital spec­traI atlas of Jacoby et aI. (Jacobi, Hunter, & Christian 1984) as template. Multivariate sta­tistical methods are .linear algorithms used for exploratory data analysis. These methods have been applied to spectral classification by using Principal Component Analysis (PCA) to reduce the dimension of the problem, followed by Clus­ter Analysis (CA) to discover groups of objects in the parameter space obtained in the previ- . ous step (Murtagh & Heck (Murtagh & Heck

. 1984) and references herein). Stellar classifica-

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tion with ANN is a new approach that has been used by von Hippel et a!. (von Hippel, Storrie­Lombardi, & Storrie-Lombardi 1994) (von Hip­pel et aI. 1994) to confirm the visual classification of the Miehigan Spectral Catalogue on objective prism spectra, determining the temperature clas­sification to better than 1.7 spectral sub classes from B3 to M4. Gulati et a!. (Gulati et ai. 1994) classify the spectral atlas of Jacoby et a!. (Jacobi, Hunter, & Christian 1984) with an accuracy of 2 spectral subclasses, based on selected spectral features.

The availability of the IUE low-dispersion archive (Wamsteker, Driessen, & Munoz 1989) allows the application of pattern recognition methods to explore the ultraviolet domain. The analysis of this archive is especially interesting, due to the homogeneity of the sample. As indi­cated by Heck (Heck et ai. 1983), it is impor­tant to remember at this point that MK spec­traI classifications defined from the visible range cannot simply be extrapolated to the ultravio­let spectral range. So far, only multivariate sta­tistieal methods have been used with IUE spec­tra. Egret and Heck (Egret & Heck 1983) analyze the relative fluxes at 16 selected wavelengths of O and B stars with PCA. Egret et al. (Egret et aI. 1984) analyze low-resolution spectra us­ing PCA on 93 variables computed as median flux values at certain wavelength bands and se­lected absorption and emission lines. These anal­yses indieate a high correlation betweeil the first principal component and the temperature. Heck · et a!. (Heck et aI. 1986) classify the IUE Low­Dispersion Spectra Reference Atlas (Heck et aI. 1983) of normal stars. Weighted intensities of sixty lines together with an asymmetry coeffi­cient describing the continuum shape are used for the classification. The algorithm consisted of PCA folIowed by CA to define different groups that confirmed the manual classification of the Atlas. Imadache and Crézé (Imadache & Crézé 1990) and Imadache (Imadache 1992) extend the sample and generalize the method, using the fulI spectral range instead of pre-selected spectral features.

The present work has been done within the context of the IUE Final Archive project. The aim is to provide an efficient and objective clas­sification procedure to explore the complete IUE database, based on methods that do not require prior knowledge about the object to be classi-

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fied. Three methods are compared: a simple met­rie distance method, a supervised ANN classifier and a unsupervised Self Organized Map (SOM) classifier. The input sample is described in sec­tion 2. The classification method based on metric distance is summarized in section 3. Section 4 ex­plains the supervised classification and section 5 describes the unsupervised method. The results are presented in section 6 and section 7 summa­rizes the conclusions.

2. The Sample Spectra

The spectra were taken from the IUE Low­Dispersion Reference Atlas of Normal Stars (Heck et aI. 1983) (hereafter the Atlas), cover­ing the wavelength range from 1150 to 3200 Á. The Atlas contains 229 normal stars distributed from the spectral type 03 to KO. The classifica­tion given in the Atlas was carried out following a classieal morphologieal approach (J aschek & Jaschek 1984), based on UV criteria alone. The set of 64 standard stars selected in the Atlas, with spectral types from 03 to G5, was used as a tem­plate in the metrie distance classification and was the training sample in ANN classification. The test set contained 163 spectra, excluding the 64 standard stars and two stars with spectral types G8 and KO, outside the spectral types covered by the training set.

The spectra were obtained by merging to­gether data from the two IUE cameras, sampled at a uniform wavelength step of 2 Á, after pro­cessing with the standard calibration pipeline. Although the spectra are good in quality, there are two aspects that seriously hinder the auto­mated classification: interstelIar extinction and contamination with geo-coronal Ly-a emission. Some pre-processing was required to eliminate these effects and to normalize the data.

AlI spectra were corrected for interstelIar ex­tinction by using Seaton's (Seaton 1979) extinc­tion law. Due to the properties of the extinction law at À1 = 1600, À2 = 2400 and Àc = 2175 Á thecolor excess E(B - V) was estimated as

The observed fluxes fI, f~ and fg were ob­tained by filtering the high frequency compo­nents in the transformed Fourier space (Lasala &

.'7.

21 SIMPÓSIO BRASILEIRO DE AUTOMAÇAO INTELIGENTE

K urtz 1985). Figure 1 shows a typical 04 spec­trum before and after correction for reddening.

Selected range

After de-reddening

1200 1600 2000 2400 2800 3200 Wavelength

Fig. 1. 'Original (top) and de-reddened (bottom) spectra corresponding to a 04 star. The selected range is indicated by the solid lines in the middle

3. Classification Using Metric Distance

Normalized spectra are considered vectors in]RN and a metric is introduced in the vector space. In this classification scheme the metric distance between the object spectrum and each spectrum in the training set is computed and the spectral class of the star in the training set having the minimum distance is assigned to the object.

Let fij = fi(Àj)j j = 1, ... , N be the flux of the i-th star in the catalogue and Skj = Sk(Àj)j j = 1, . .. , N be the flux of the k-th stan­dard star in the training set, after correction for reddening and normalization. The distance, dik,

is defined by

N 2 1 ~ 2

dik = N L.J(!ij - Skj) . j=l

(2)

4. Supervised Classification Using ANN

A supervised classification scheme based on arti­ficial neural networks (ANN) has been used. This techl1ique was originally developed by McCul-10gh and Pitts (McCullogh & Pitts 1943) and has been generalized with an algorithm for training

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Flux of information

Output Layer

Input Layer

Fig. 2. A typical ANN topology

networks having multiple layers, known as back­propagation (Rumelhart, Hinton, & Williams 1986). In a general form, a neural network repre­sents a function, F, that maps a given input set into a selected output set. Assuming that normal­ized spectra are elements in a N -dimensional vec­tor space and spectral classes are defined by M­dimensional classification vectors, the network approximates the mapping F : mN --* ]R M ,

in such a way that a standard star, S k, is as­sociated with the vector Ck = F(Sk)' The out­put vector defin,es the spectral class so that 00 is given by (1, O, O, . .. ,O), 01 is represented by (0,1,0, . .. ,O) and so on. In this form, the net­work can be regarded as a classifier that maps the input space of normalized fluxes into Iof M, Le., one output unity and all others zero. Such a network, with a squared-error cost function, gives a good estimation of Bayesian probabili­ties (Richard & Lippmann 1991), so that ·for an input spectrum J, the i-th component of the out­put vector is the probability P(CiIJ) for class i given the input spectrum. In the Figure 2 is rep­resented a typical ANN topology.

5. Unsupervised Classification Using SOM

In the Self Organized Map (SOM) the net or­ganizes the spectra into clusters based on sim­ilarities using a metric to define the distance

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between two spectra. The algorithm used to per­form such clustering was developed by Kohonen (Kohonen 1984).

A schematic Self Organized Map (SOM) is shown in Figure 3. In this representation the input layer is shown with 3 neurons and a bi­dimensional net with 9 neurons. The output values are represented by the vertical arrows. Each input neuron is full connected to the bi­dimensional neto

Output

Input Layer

Bi-Dimensional Net

Fig. 3. Representation of a bi-dimensional SOM.

6. RESULTS

6.1. ANN

The resuIts obtained for different architectures compared with the Atlas are shown in Table 1, where r is the correlation coefficient and u is the standard deviation. The distribution of discrep­andes between the manual classification and the automated methods are shown in Figure 5 for ANN and Metric Distance. In the Figure 5 is shown the results of the classification for the first configuration in the Table 1. The configuration having 120 nodes and 2 hidden layers was used to compare ANN and metric distance. There is a good agreement between the this two classifica­tion methods.

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40

20

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_ANN D Melric Distance

o~~~~~~~~~~~~~

·5 -4 -3 -2 -1 o 234 5 Error

~21~1

Fig. 4. Distribution for classification discrepancies for ANN and Metric Distance versus Atlas

G r-----------------------------~

GlF ~ üi õA .g ãí ~B

B A Atlas

F G

G r---------------------------~

F

z ~A

B

B A Atlas

F G

G .---------------------------~

F

z ~A

B

B A F G Metric Distance

Fig. 5. Results of classification: Metric Distance ver­sus Atlas (top), ANN versus Atlas (middle) and ANN versus Metric Distance (bottom). The solid lines are drawn just for reference

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Hidden Hidden Nodes Layers r

120 2 0.988 60 2 0.983 30 2 0.946 120 1 0.984 60 1 0.986 30 1 0.982

Table 1. Network Configurations

6.2. SOM

u

1.107 1.350 2.379 1.313 1.221 1.378

In this work it was used a 8x8 bi-dimensional net with 744 neurons in the input layer. The main set of spectra was exactly the same used in the supervised classification. The classifier gives an error of 1.62 sub classes if compared with the At­las, with a correlation of 0.9844. In addition, 27 stars could not be classified according to the clas­sification criterium used in this experimento The adopted criterium uses standard stars as labels. If a neuron in the bi-dimensional plane is not associated with some of the 64 standard stars, none of the stars assigned to this neuron by the net will are classified.

K

G

~F o (J)A

B

o o B A K Alia

K

G

~F o (J)A

B

o o B A ANN

Fig. 6. Results of classification: SOM versus Atlas (top), SOM versus' ANN (bottom). The solid lines are drawn just for reference

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7. CONCLUSIONS

- The automated classification can be applied to large databases and the errors are compat­ible with the ones found in manual classifi­cation methods. The error found for super­vised algorithm is of 1.10 subclasses and of 1.62 subclasses for the unsupervised method.

- The main advantage of the two methods applied in this work is that both methods use the spectra as observed without previous analysis of spectral features.

- In addition, the unsupervised classification doesn 't need a priori know ledge to perform the classification.

- Furthermore, no personal criteria are used and that the classification can be reproduced, which in general is not possibIe in classifica­tion made by human experts.

- The methods are robust enough to be used in case of spectra with missing information and further improvements can be obtained with IUE spectra rejecting bad pixels as indicated in the quality flags associated with the spec­traI values.

- This research will be continued to derive physical parameters by using stellar models in connection with observed spectra, and taking into account Iuminosity classes.

References

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