A ``maximum-path''-based classification (Q2711719)

It is common knowledge that equivalence exists between the single linkage dendrogram and the minimum spanning tree. Various criticisms have been directed towards the results of single-link analysis. In this paper, the minimum spanning tree as a useful tool showing privileged directions to single out isolated points, clusters and stable clusters is considered. The maximum path contains most points of the minimum spanning tree. The major property of the maximum path consists of being the ``longest path'' with regard to all possible ones. Besides, the method of maximum path and its linearization as a useful basis of reference to classify the points is proposed.NEWLINENEWLINENEWLINEThe properties of the minimum spanning tree together with the projections of the lateral vertices on the maximum ~path with reference to the ultrametric distance assures the ~correctness and the validity of the classification with barriers. The suggested algorithms are computationally efficient and they can be used in a lot of applications.