@article {IOPORT.06055533,
    author       = {Carlsson, Gunnar and M\'{e}moli, Facundo},
    title        = {Characterization, stability and convergence of hierarchical clustering methods.},
    year         = {2010},
    journal      = {Journal of Machine Learning Research (JMLR)},
    volume       = {11},
    issn         = {1532-4435},
    pages        = {1425-1470},
    publisher    = {Microtome Publishing, Brookline, MA},
    abstract     = {Summary: We study hierarchical clustering schemes under an axiomatic view. We show that within this framework, one can prove a theorem analogous to one of Kleinberg (2002), in which one obtains an existence and uniqueness theorem instead of a non-existence result. We explore further properties of this unique scheme: stability and convergence are established. We represent dendrograms as ultrametric spaces and use tools from metric geometry, namely the Gromov-Hausdorff distance, to quantify the degree to which perturbations in the input metric space affect the result of hierarchical methods.},
    identifier   = {06055533},
}