The purpose of this project is to respond to an actual necessity -- the need to discover knowledge from huge data collection comprising multiple sequences that evolve over time -- by proposing a methodology for temporal rule extraction. To obtain what we called temporal rules, a discretisation phase that extracts events from raw data is applied first, followed by an inference phase, where classification trees are constructed based on these events. The discrete and continuous characteristics of an event, according to its definition, allow the use of statistical tools as well as of techniques from artificial intelligence on the same data.

A theoretical framework for this methodology, based on first-order temporal logic, is also defined. This formalism permits the definition of the main notions (event, temporal rule, constraint) in a formal way. The concept of consistent linear time structure allows us to introduce the notions of general interpretation, of support and of confidence, the lasts two measures being the expression of the two similar concepts used in data mining. These notions open the possibility to use statistical approaches in the design of algorithms for inferring higher order temporal rules, denoted temporal meta-rules.

The capability of the formalism is extended to "capture" the concept of time granularity. To keep an unitary viewpoint of the meaning of the same formula at different time scales, the usual definition of the interpretation for a predicate symbol, in the frame of a temporal granular logic, is changed: it returns now the degree of truth (a real value between zero and one) and not the meaning of truth (one of the values true or false).

Finally, a probabilistic model is attached to the initial formalism to define a stochastic first-order temporal logic. By using advanced theorems from the stochastic limit theory, it was possible to prove that a certain amount of dependence (called near-epoch dependence) is the highest degree of dependence which is sufficient to induce the property of consistency.

• Start date : 01.04.2001
• End date : 30.09.2003
• Amount : 103 068 CHF
• Financing : Fonds National Suisse

[1] P. Cotofrei and K. Stoffel, "Rule Extraction from Time Series Databases using Classification Trees", Proceedings of IASTED International Conference on Applied Informatics, Innsbruck, February 2002, pp. 327-332.

[2] P. Cotofrei and K. Stoffel, "Classification Rules + Time = Temporal Rules", Proceedings of International Conference on Computational Science, Amsterdam, LNCS 2329, April 2002, pp. 572-581.

[3] P. Cotofrei and K. Stoffel, "A Formalism for Temporal Rules", In Proceedings of Temporal Data Mining Workshop, 8th ACM SIGKDD Conference, Edmonton, Canada, August 2002, pp. 25-37.

[4] P. Cotofrei and K. Stoffel, "First-Order Logic Based Formalism for Temporal Data Mining", Proceedings of IEEE ICMD02 Workshop on Foundations of Data Mining and Knowledge Discovery, Maebashi, Japan, December 2002, pp. 101-106.

[5] P. Cotofrei and K. Stoffel, "Higher Order Temporal Rules", Proceedings of International Conference on Computational Science, St. Petersburg, LNCS 2329, June 2003, pp. 323-332.

[6] P. Cotofrei and K. Stoffel, "From Temporal Rules to Temporal Meta-Rules", Proceedings of DaWak Conference, Zaragoza, Spain, LNCS 3181, September 2004, pp. 169-178.

[7] P. Cotofrei and K. Stoffel, "Temporal granular logic for temporal data mining", Proceedings of IEEE International Conference on Granular Computing, Vol. 2, 2005, pp. 417-422.

[8] P. Cotofrei and K. Stoffel, "Stochastic Processes and Temporal Rules", Proceedings of IEEE Granular Computing 2006, Atlanta, USA, May 2006, pp. 435-440.

[9] P. Cotofrei and K. Stoffel, "Stochastic Processes and Temporal Data Mining", Proceedings of the 13th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, San Jose, August 2007, pp.183-190.

[1] P. Cotofrei and K. Stoffel, First-Order Logic Based Formalism for Temporal Data Mining ,  chapter in "Foundation of Data Mining and Knowledge Extraction", series Studies in Computational Intelligence, T.Y. Lin and C.J. Liau ed., vol 6/2005, Springer Verlag, pp. 185-210, ISBN: 978-3-540-26257-2.

[2] P. Cotofrei and K. Stoffel, Time Granularity in Temporal Data Mining , chapter in "Foundations of Computational Intelligence Volume 6: Data Mining", series Studies in Computational Intelligence, A. Abraham, Andre de Carvalho and V. Snasel ed., 2009, Springer Verlang, pp. 67-96, ISBN: 978-3-642-01090-3.

[3] P. Cotofrei and K. Stoffel, Temporal Rules over Time Structures with Different Granularities - a Stochastic Approach,  chapter in "New Fundamental Technologies in Data Mining", K. Funatsu ed., InTech, 2011, pp. 447-466, ISBN: 978-953-307-547-1.