Learning representations from dendrograms

Random Dendrograms

An attempt is made to create some statistical tests for comparing results of hierarchical cluster analysis based on the uniform distribution over the set of all possible dendrograms. Three different uniform distributions are considered according to the degree of similarity of the dendrograms. Some distances between dendrograms are defined and The solutions proposed are computational and are bas...

Mumford Dendrograms

An effective p-adic encoding of dendrograms is presented through an explicit embedding into the Bruhat-Tits tree for a p-adic number field. This field depends on the number of children of a vertex and is a finite extension of the field of p-adic numbers. It is shown that fixing p-adic representatives of the residue field allows a natural way of encoding strings by identifying a given alphabet w...

Decoupling Learning Rules from Representations

In the artificial intelligence field, learning often corresponds to changing the param-eters of a parameterized function. A learning rule is an algorithm or mathematicalexpression that specifies precisely how the parameters should be changed. Whencreating an artificial intelligence system, we must make two decisions: what repre-sentation should be used (i.e., what parameterized ...

Structural Learning from Iconic Representations

Trees, Dendrograms and Sensitivity

Dendrograms and minimum-weight spanning trees (MWST) are discrete structures which arise in clustering theory, networks, and where strategic choices are made between discrete options. The discrete structure of the solution tree varies discontinuously with respect to changes in the dissimilarity or cost matrix. Tarjan [1982] has obtained bounds on the changes to the elements of the cost matrix, ...