We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function of the distance between the neighbors. This magnetic system
exhibits three phases. At very low temperatures it is completely ordered; all
spins are aligned. At very high temperatures the system does not exhibit any
ordering and in an intermediate regime clusters of relatively strongly coupled
spins become ordered, whereas different clusters remain uncorrelated. This
intermediate phase is identified by a jump in the order parameters. The
spin-spin correlation function is used to partition the spins and the
corresponding data points into clusters. We demonstrate on three synthetic and
three real data sets how the method works. Detailed comparison to the
performance of other techniques clearly indicates the relative success of our
method.Comment: 46 pages, postscript, 15 ps figures include