  Mean shift clustering finds the modes of the data probability density by
identifying the zero points of the density gradient. Since it does not require
to fix the number of clusters in advance, the mean shift has been a popular
clustering algorithm in various application fields. A typical implementation of
the mean shift is to first estimate the density by kernel density estimation
and then compute its gradient. However, since good density estimation does not
necessarily imply accurate estimation of the density gradient, such an indirect
two-step approach is not reliable. In this paper, we propose a method to
directly estimate the gradient of the log-density without going through density
estimation. The proposed method gives the global solution analytically and thus
is computationally efficient. We then develop a mean-shift-like fixed-point
algorithm to find the modes of the density for clustering. As in the mean
shift, one does not need to set the number of clusters in advance. We
empirically show that the proposed clustering method works much better than the
mean shift especially for high-dimensional data. Experimental results further
indicate that the proposed method outperforms existing clustering methods.
