Entropy approach to the construction of a measure of word symbolic diverseness and its application to clustering of plant genomes

An approach to the information analysis is considered for the case when the information is presented by words of finite length over a finite alphabet. A method of generating a measure of symbolic diverseness of words based on peak characteristics of a shift entropy function is proposed. The shift entropy function is formally defined using a unit translation operator and the entropy of discrete distributions. A model example is presented together with some results of application of the proposed measure in the clustering of families of plants using the analysis of genome of their representatives.