  We perform an objective classification of 170,000 galaxy spectra in the Sloan
Digital Sky Survey (SDSS) using the Karhunen-Lo\`eve (KL) transform. With about
one-sixth of the total set of galaxy spectra which will be obtained by the
survey, we are able to carry out the most extensive analysis of its kind to
date. The formalism proposed by Connolly and Szalay is adopted to correct for
gappy regions in the spectra, and to derive eigenspectra and eigencoefficients.
  From this analysis, we show that this gap-correction formalism leads to a
converging set of eigenspectra and KL-repaired spectra. Furthermore, KL
eigenspectra of galaxies are found to be convergent not only as a function of
iteration, but also as a function of the number of randomly selected galaxy
spectra used in the analysis. From these data a set of ten eigenspectra of
galaxy spectra are constructed, with rest-wavelength coverage 3450-8350
angstrom. The eigencoefficients describing these galaxies naturally place the
spectra into several classes defined by the plane formed by the first three
eigencoefficients of each spectrum. Spectral types, corresponding to different
Hubble-types and galaxies with extreme emission lines, are identified for the
170,000 spectra and are shown to be complementary to existing spectral
classifications. From a non-parametric classification technique, we find that
the population of galaxies can be divided into three classes which correspond
to early late- through to intermediate late-types galaxies. (Abridged)
