Stochastic processes and temporal data mining

ABSTRACT

This article tries to give an answer to a fundamental question intemporal data mining: "Under what conditions a temporal rule extracted from up-to-date temporal data keeps its confidence/support for future data". A possible solution is given by using, on the one hand, a temporal logic formalism which allows the definition of the main notions (event, temporal rule, support, confidence) in a formal way and, on the other hand, the stochastic limit theory. Under this probabilistic temporal framework, the equivalence between the existence of the support of a temporal rule and the law of large numbers is systematically analyzed.

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INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.8 Database applications
          Subjects: Data mining

Additional Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.1 Mathematical Logic
          Subjects: Temporal logic

  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Stochastic processes

General Terms:
Theory

Keywords:
consistency of temporal rules, stochastic limit theory, stochastic processes, temporal data mining, temporal logic formalism