Average Consensus and Infinite Norm Consensus : Two Methods for Ultrametric Trees

Abstract

Consensus methods are widely used to combine hierarchies defined on a common set of n object. Many methods have been proposed during the last decade to combine hierarchies. One of these, the average consensus method, allows one to obtain a consensus solution that is representative of the initial profile of trees by minimizing the sum of the squared distances between this profile and the consensus solution. This problem is known to be NP-complete and one has to rely on heuristics to obtain a consensus result in such cases. As a consequence, the uniqueness and optimality of the solution is not guaranteed. The L∞-consensus that yields to a universal solution in a maximum of n 2 steps is an alternative to the average consensus procedure. The two methods will be presented and compared on a numerical example.KeywordsConsensus MethodCophenetic CorrelationUniversal SolutionAverage ConsensusSystematic ZoologyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.