  We propose a Fourier-based approach for optimization of several clustering
algorithms. Mathematically, clusters data can be described by a density
function represented by the Dirac mixture distribution. The density function
can be smoothed by applying the Fourier transform and a Gaussian filter. The
determination of the optimal standard deviation of the Gaussian filter will be
accomplished by the use of a convergence criterion related to the correlation
between the smoothed and the original density functions. In principle, the
optimal smoothed density function exhibits local maxima, which correspond to
the cluster centroids. Thus, the complex task of finding the centroids of the
clusters is simplified by the detection of the peaks of the smoothed density
function. A multiple sliding windows procedure is used to detect the peaks. The
remarkable accuracy of the proposed algorithm demonstrates its capability as a
reliable general method for enhancement of the clustering performance, its
global optimization and also removing the initialization problem in many
clustering methods.
