  We present the results from several studies used to search for astrophysical
sources of high-energy neutrinos using the Super-Kamiokande-I (April 1996 to
July 2001) neutrino-induced upward-going muon data. The data set consists of
2359 events with minimum energy 1.6 GeV, of which 1892 are through-going and
467 stop within the detector. The results of several independent analyses are
presented, including searches for point sources using directional and temporal
information and a search for signatures of cosmic-ray interactions with the
interstellar medium in the upward-going muons. No statistically significant
evidence for point sources or any diffuse flux from the plane of the galaxy was
found, so specific limits on fluxes from likely point sources are calculated.
The 90% C.L. upper limits on upward-going muon flux from astronomical sources
which are located in the southern hemisphere and always under the horizon for
Super-Kamiokande are 1~4x10^{-15} cm^{-2} s^{-1}.
