The Zipf Law revisited: An evolutionary model of emerging classification

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:466434

Levitin, L B ^[1]; Schapiro, B ^[2]; Perlovsky, L ^[3]

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1. Boston Univ., MA (United States)
2. TINA, Brandenburg (Germany)
3. NRC, Wakefield, MA (United States)

Zipf`s Law is a remarkable rank-frequency relationship observed in linguistics (the frequencies of the use of words are approximately inversely proportional to their ranks in the decreasing frequency order) as well as in the behavior of many complex systems of surprisingly different nature. We suggest an evolutionary model of emerging classification of objects into classes corresponding to concepts and denoted by words. The evolution of the system is derived from two basic assumptions: first, the probability to recognize an object as belonging to a known class is proportional to the number of objects in this class already recognized, and, second, there exists a small probability to observe an object that requires creation of a new class ({open_quotes}mutation{close_quotes} that gives birth to a new {open_quotes}species{close_quotes}). It is shown that the populations of classes in such a system obey the Zipf Law provided that the rate of emergence of new classes is small. The model leads also to the emergence of a second-tier structure of {open_quotes}super-classes{close_quotes} - groups of classes with almost equal populations.

• OSTI ID: 466434
• Report Number(s): CONF-9610138--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ARTIFICIAL INTELLIGENCE
MARKOV PROCESS
MUTATIONS
PATTERN RECOGNITION
PROBABILITY
PROGRAMMING LANGUAGES
STATISTICAL MODELS