Nearest-neighbors medians clustering Articles uri icon

publication date

  • August 2012

start page

  • 349

end page

  • 362

issue

  • 4

volume

  • 5

international standard serial number (ISSN)

  • 1932-1864

electronic international standard serial number (EISSN)

  • 1932-1872

abstract

  • We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of clusters and the partition of the observations given the proportion alfa of neighbors. A fast version of the algorithm where only a subset of the observations from the sample is processed is also proposed. A proof of the convergence from each point to its closest fixpoint and the existence and uniqueness of a fixpoint in a neighborhood of each mode is given for the univariate case