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8 Results and discussion

The field studied here contains the associations NGC 456, NGC 460 a,b and NGC 465 of SMC. These associations occupy only $10\%$ of the studied region. The majority of the stellar spectrum owing to the associations, superimposed to HII regions, has been saturated and excluded from our sample. The accuracy of this classification is $\pm 1$ spectral type (Dapergolas et al. [1991]).

The method has been tested on spectra for which a visual classification was available. The down limit for the faint spectra was the same as in visual classification. For the bright spectra the limit has been described in Sect. 3. The method has been developed on photographic objective prism plates but it can be equally be well applied to CCD objective prism images.

The results from human expert (HE), linear correlation (LC) and minimum distance (MD) method are shown in Table 3. Figures 10-12 show the histograms for each method.


Table 3: Details for the different classification methods
Spectral Type ${\rm OB}$ A F G K M
Class 1 2 3 4 5 6
HE 150 63 19 47 63 84
LC 148 48 32 61 62 75
MD 145 41 38 64 65 73

\psfig{,height=60mm,width=80mm} }
\vspace{5mm} \end{figure} Figure 10: Histogram for the human classifier

\psfig{,height=60mm,width=80mm} }
\vspace{5mm} \end{figure} Figure 11: Histogram for the linear correlation method

\psfig{,height=60mm,width=80mm} }
\vspace{5mm} \end{figure} Figure 12: Histogram for the minimum distance method

To quantify the degree of agreement between different classification methods we have calculated the mean error $me_{{\rm hehe}}$ between two human experts a and b, $me_{{\rm helc}}$ between human expert and linear correlation classification and $me_{{\rm hemd}}$ between human expert and minimum distance classification and the corresponding dispersions $\sigma_{{\rm hehe}}$, $\sigma_{{\rm helc}}$ and $\sigma_{{\rm hemd}}$using the following equations

$\displaystyle {me_{{\rm hehe}}}$ = $\displaystyle \frac{1}{426}\displaystyle\sum_{i=1}^{426}\mid C_{{\rm he(a)}}^{i}-C_{{\rm he(b)}}^{i}\mid$  
  = 0.23  

$\displaystyle {me_{{\rm helc}}}$ = $\displaystyle \frac{1}{426}\displaystyle\sum_{i=1}^{426}\mid C_{{\rm he}}^{i}-C_{{\rm lc}}^{i}\mid$  
  = 0.27  

$\displaystyle {me_{{\rm hemd}}}$ = $\displaystyle \frac{1}{426}\displaystyle\sum_{i=1}^{426}\mid C_{{\rm he}}^{i}-C_{{\rm md}}^{i}\mid$  
  = 0.29  

$\displaystyle {\sigma_{{\rm hehe}}}$ = $\displaystyle \sqrt{\frac{1}{426}\displaystyle\sum_{i=1}^{426}(C_{{\rm he(a)}}^{i}-C_{{\rm he(b)}}^{i})^2}$  
  = 0.47  

$\displaystyle {\sigma_{{\rm helc}}}$ = $\displaystyle \sqrt{\frac{1}{426}\displaystyle\sum_{i=1}^{426}(C_{{\rm he}}^{i}-C_{{\rm lc}}^{i})^2}$  
  = 0.58  


$\displaystyle {\sigma_{{\rm hemd}}}$ = $\displaystyle \sqrt{\frac{1}{426}\displaystyle\sum_{i=1}^{426}(C_{{\rm he}}^{i}-C_{{\rm md}}^{i})^2}$  
  = 0.60.  


Table 4: Statistical properties for the different classification methods
Test mean error dispersion
hehe 0.23 0.47
helc 0.27 0.58
hemd 0.29 0.60

For comparison reasons, we display these results in Table 4. The two automated methods of classification seem to be close to the human expert classification for the low-dispersion prism (P1) stellar spectra with linear correlation giving better results. An extended study for classification with artificial neural networks is under preparation.

This research has been supported by a grant from the General Secretariat of Research and Technology of Greece, PENED program. The authors are grateful to the UK Schmidt Telescope Plate Library (ROE) for the loan of the observational material.

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