@techreport{TR-IC-07-31,
  number = {IC-07-31},
  author = {Leonardo M. Rocha and
            Alexandre X. Falcão and
            Luis G. P. Meloni},
  title = {Data Clustering based on Optimum-Path Forest and Probability Density Function},
  month = {October},
  year = {2007}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 20 pages.
    \par\selectlanguage{english}\textbf{Abstract}
        The identification of natural groups in a dataset is reduced to an
        \emph{optimum-path forest} problem in a graph. We define a graph
        whose nodes are data samples and whose arcs connect \emph{adjacent}
        samples in a feature space. The nodes are weighted by their
        probability density values and different choices of a
        \emph{path-value function} lead to effective solutions for data
        clustering. The method identifies a root node for each cluster and
        finds the samples which are ``more strongly connected'' to each root
        than to any other. The output is an optimum-path forest whose trees
        (clusters) are the influence zones of their roots. This framework
        extends the image foresting transform from the image domain to the
        feature space, revealing important theoretical relations among
        relative fuzzy-connected segmentation, morphological
        reconstructions, watershed transforms, and clustering by influence
        zones. It also provides a more general and robust implementation for
        the popular mean-shift algorithm. The results are illustrated in
        image segmentation.
  }
}