• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Об одном характеристическом функционале слов над конечным алфавитом

Ульянов М. В., Сметанин Ю. Г.

The objects studied in the article are finite words over some finite alphabet. These words are symbolical codes of the investigated objects and processes that are analyzed further. A formalization of the entropy on words function is proposed that is based on the of the entropy of discrete distributions. Using the results of analysis of sets of words with fixed length over a given alphabet,  a notion of entropy function majorant is proposed. The entropy on words function and the majorant form the basis for the forms of a characteristic functional proposed in the article, which give a quantitative estimation of the proximity of the tested finite word to a subword of the same length, randomly selected from a random infinite word over the same alphabet. The proposed forms of the functional may be used for solving different tasks of data analysis, including clustering and pattern recognition tasks.