Consensus functions defined on trees

Analysing molecular sequences using consensus

“…Since being introduced in the 1970s and extensively studied in the 1980s, consensus methods for trees have proved to be useful tools in systematics. Consensus methods, such as majority rule, are used in analyses of rooted trees with labelled leaves by Margush & McMorris (1981), McMorris & Neumann (1983), and Barthelemy & McMorris (1986). An entire issue of the Journal of Class(fication featured papers about consensus classifications (Day 1986), notable among them the review by of how ordered set theory provides both framework and tools for investigating problems on the consensus and comparison of classifications.…”

On the use of ordered sets in problems of comparison and consensus of classifications

“…In the following sections, we recall or establish properties of polynomial rules One has to observe that, sometimes, these rules do not give interesting consensus classifications For instance, when the n-trees of a profile 7r E T~ are too different, the majority rule n-tree is the bush T~ with only trivial clusters Several nonpolynomial consensus methods on n-trees have been proposed (Adams 1972, Neumann 1983, Stinebrickner 1984, Finden and Gordon 1985, Neumann and Norton 1985. Though the properties of these methods are not always clear, they may give nontrivial consensus ntrees in situations where polynomial rules do not work satisfactorily One may use a consensus index (see Section 3 4) in order to avoid using a consensus n-tree when the elements of the profile are irreconcilable The situation is quite the same in the cases of ordered trees or Buneman trees…”

Consensus Decision Trees: Using Consensus Hierarchical Clustering for Data Relabelling and Reduction

“…In the last thirty years many consensus clustering methods have been proposed (e.g., Regnier, 1965;Adams, 1972;McMorris and Neuman, 1983;Day, 1983). In 1986, a special issue of the Journal of Classification was devoted to consensus classifications.…”