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<H2><A NAME="SECTION00553000000000000000">
Multivariate Statistical Methods</A>
</H2>
When the analysis yields a large number of parameters for each object,
it is difficult to overview relations between the individual variable.
Multivariate statistical methods can be applied in such a situation to
give an objective description of the data. The Principal Components
Analysis is used to determine the true dimensionality of the data set
and find the best linear combination of the parameter for following
studies (see Chatfield and Collins 1980). A typical example of such
analysis was performed by Okamura (1985) on photometric data from
Virgo Cluster galaxies.
<P>
Structures and groups in large data sets can be located by means of a
Cluster Analysis which constructs a set of groups in the data using a
given distance measure. A large variety of methods for clustering are
available with different distance definitions providing both
hierarchical and non-hierarchical groups (see Murtagh 1986 and
references therein). These techniques are used especially for
classification problems in astronomy.
<P>
<DIV ALIGN="CENTER"><B><FONT SIZE="+2"> References</FONT></B></DIV>
<UL>
<LI> Baker, A.E. : 1925, <I>Proc. Roy. Soc. Edingburgh</I> <B>45</B> 166.
<LI> Bijaoui, A. : 1981, <I>Image et information</I>, Masson, Paris.
<LI> Bevington, P.R. : 1969, <I>Data Reduction and Error Analysis for
the Physical Sciences</I>, McGraw-Hill, New York.
<LI> Capaccioli, M., Held, E. : 1983, private communication.
<LI> Chatfield, C., Collins, A.J. : 1980, <I>Introduction to Multivariate
Analysis</I>, Chapman and Hall.
<LI> Frieden, B.R. : 1972, <I>J. Opt. Soc. Am.</I> <B>62</B>, 511.
<LI> Goad, L.E. : 1980, <I>SPIE</I> <B>264</B>, 136.
<LI> Grosbøl, P. : 1979, <I>Image Processing in Astronomy</I>,
Eds. G. Sedmark, M. Capaccioli, R.J. Allen,
Osservatorio Astronomico di Trieste, p. 371.
<LI> Grosbøl, P. : 1980, <I>SPIE</I> <B>264</B>, 118.
<LI> Helstrom, C.W. : 1967, <I>J. Opt. Soc. Am.</I> <B>57</B>, 297.
<LI> Herzog, A.D., Illingworth,G. : 1977, <I>Astrophys. J. Suppl.</I>
<B>33</B>, 55.
<LI> Horner, J.L. : 1970, <I>Applied Op.</I> <B>9</B>, 167.
<LI> Lucy, L.B. : 1974, <I>Astron. J.</I> <B>79</B>, 745.
<LI> Martin, R., Lutz,R.K. : 1979, <I>Image Processing in Astronomy</I>,
Eds. G. Sedmark, M. Capaccioli, R.J. Allen,
Osservatorio Astronomico di Trieste, p. 211.
<LI> Murtagh, F. : 1986, <I>ESO Preprint No.</I> <B>448</B>
<LI> Newell, E.B. : 1979, <I>Image Processing in Astronomy</I>,
Eds. G. Sedmark, M. Capaccioli, R.J. Allen,
Osservatorio Astronomico di Trieste, p. 100.
<LI> Newell, B., O'Neil, Jr., E.J. : 1977, <I>Pub. Astron. Soc. Pac.</I>
<B>89</B>, 925.
<LI> Okamura, S. : 1985, <I>Proc. of ESO Workshop on The Virgo Cluster</I>,
Eds. O.-G. Richter and B. Binggeli, ESO, p. 201.
<LI> Pratt, N.M. : 1977, <I>Vistas in Astronomy</I> <B>21</B>, 1.
<LI> Pratt, W.K. : 1978, <I>Digital Image Processing</I>, Wiley-Interscience,
New York.
<LI> Rosenfeld, A., Kak, A.C. : 1982 <I>Digital Picture Processing</I>
Vol. <B>1-2</B>, Academic Press, New York.
<LI> Tukey, J.W. : 1971, <I>Exploratory Data Analysis</I>, Addison-Wesley,
Reading, Mass.
<LI> Wells, D.C. : 1980, <I>SPIE</I> <B>264</B>, 148.
</UL>
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=31 =3 =1999
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-15</I>
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