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Fast time intervals mining using the transitivity of temporal relations

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Abstract

We introduce an algorithm, called KarmaLego, for the discovery of frequent symbolic time interval-related patterns (TIRPs). The mined symbolic time intervals can be part of the input, or can be generated by a temporal-abstraction process from raw time-stamped data. The algorithm includes a data structure for TIRP-candidate generation and a novel method for efficient candidate-TIRP generation, by exploiting the transitivity property of Allen’s temporal relations. Additionally, since the non-ambiguous definition of TIRPs does not specify the duration of the time intervals, we propose to pre-cluster the time intervals based on their duration to decrease the variance of the supporting instances. Our experimental comparison of the KarmaLego algorithm’s runtime performance with several existing state of the art time intervals pattern mining methods demonstrated a significant speed-up, especially with large datasets and low levels of minimal vertical support. Furthermore, pre-clustering by time interval duration led to an increase in the homogeneity of the duration of the discovered TIRP’s supporting instances’ time intervals components, accompanied, however, by a corresponding decrease in the number of discovered TIRPs.

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Notes

  1. Karma—The law of cause and effect originated in ancient India and is central to Hindu and Buddhist philosophies.

  2. Lego—A popular game, in which modular bricks are used to construct different objects.

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Acknowledgments

The authors wish to thank Panagiotis Papapetrou for sharing datasets and insightful discussions, as well as Christos Faloutsos, Christian Freksa, Frank Hoppner, Fabian Moerchen and Dhaval Patel for insightful discussions about time intervals mining. This work was supported in part by grants from the Deutsche Telekom Laboratories at Ben Gurion University, and by the HP labs Innovation Research Program, Award No. 2008-1023.

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Authors and Affiliations

  1. Department of Information Systems Engineering, Ben Gurion University, Beersheba, Israel

    Robert Moskovitch & Yuval Shahar

  2. Telekom Innovation Laboratories, Ben Gurion University, Beersheba, Israel

    Robert Moskovitch

  3. Department of Biomedical Informatics, Systems Biology and Medicine, Columbia University, New York, NY, USA

    Robert Moskovitch

Authors
  1. Robert Moskovitch
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  2. Yuval Shahar
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Corresponding author

Correspondence to Robert Moskovitch.

Appendix

Appendix

Table 3 contains the cutoff definitions used for each state in the case of the raw measurements included in the Diabetes dataset. The rest of the raw data consisted of medications, for each of which an overall defined daily dose (DDD) abstraction was defined.

Table 3 Measurement data types and their cut-off (discretization) values for 3 or 4 state abstractions each, for four concepts, in the case of the diabetes data set
Full size table

The knowledge-based state-abstraction definitions for the measurements were provided by physicians from Ben Gurion University’s Soroka Medical Center.

In the following four parts of Table 3, the cutoff definitions are presented for each state for the various temporal measurement variables in the Diabetes dataset.

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Moskovitch, R., Shahar, Y. Fast time intervals mining using the transitivity of temporal relations. Knowl Inf Syst 42, 21–48 (2015). https://doi.org/10.1007/s10115-013-0707-x

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