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Exceptionally monotone models—the rank correlation model class for Exceptional Model Mining

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Abstract

Exceptional Model Mining strives to find coherent subgroups of the dataset where multiple target attributes interact in an unusual way. One instance of such an investigated form of interaction is Pearson’s correlation coefficient between two targets. EMM then finds subgroups with an exceptionally linear relation between the targets. In this paper, we enrich the EMM toolbox by developing the more general rank correlation model class. We find subgroups with an exceptionally monotone relation between the targets. Apart from catering for this richer set of relations, the rank correlation model class does not necessarily require the assumption of target normality, which is implicitly invoked in the Pearson’s correlation model class. Furthermore, it is less sensitive to outliers. We provide pseudocode for the employed algorithm and analyze its computational complexity, and experimentally illustrate what the rank correlation model class for EMM can find for you on six datasets from an eclectic variety of domains.

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Notes

  1. Whether this model class falls under the spirit of EMM is debatable; having only a single target prohibits investigating target interaction. Careful reading of EMM literature [4, 5] reveals that the framework (accidentally) allows model classes where \(m=1\). Hence, we cannot formally say that this model class doesn’t fall under the letter of EMM. Since the authors of [12] introduced this model class as an EMM instance, and we cannot formally reject it as such, we adopt it into the EMM canon.

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Acknowledgments

We would like to thank Dr. Johannes Albrecht (Emmy Noether group leader at the TU Dortmund, department of experimental physics, with research focus on the CERN LHCb Experiment) for fruitful discussion and helpful comments. This research is supported in part by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB 876 “Providing Information by Resource-Constrained Analysis,” Project A1. This work was supported by the European Union through the ERC Consolidator Grant FORSIED (Project Reference 615517).

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  1. Fakultät für Informatik, LS VIII, Technische Universität Dortmund, Dortmund, Germany

    Lennart Downar

  2. Data Science Lab and iMinds, Universiteit Gent, Gent, Belgium

    Wouter Duivesteijn

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  1. Lennart Downar
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  2. Wouter Duivesteijn
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Correspondence to Wouter Duivesteijn.

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Downar, L., Duivesteijn, W. Exceptionally monotone models—the rank correlation model class for Exceptional Model Mining. Knowl Inf Syst 51, 369–394 (2017). https://doi.org/10.1007/s10115-016-0979-z

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