  We propose a new soft clustering scheme for classifying galaxies in different
activity classes using simultaneously 4 emission-line ratios; log([NII ]/Ha),
log([SII]/Ha), log([OI]/Ha) and log([OIII]/Hb). We fit 20 multivariate Gaussian
distributions to the 4-dimensional distribution of these lines obtained from
the Sloan Digital Sky Survey (SDSS) in order to capture local structures and
subsequently group the multivariate Gaussian distributions to represent the
complex multi-dimensional structure of the joint distribution of galaxy spectra
in the 4 dimensional line ratio space. The main advantages of this method are
the use of all four optical-line ratios simultaneously and the adoption of a
clustering scheme. This maximises the available information, avoids
contradicting classifications, and treats each class as a distribution
resulting in soft classification boundaries and providing the probability for
an object to belong to each class. We also introduce linear multi-dimensional
decision surfaces using support vector machines based on the classification of
our soft clustering scheme. This linear multi-dimensional hard clustering
technique shows high classification accuracy with respect to our
soft-clustering scheme.
