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Novel similarity measure for interval-valued data based on overlapping ratio

Kabir, Shaily; Wagner, Christian; Havens, Timothy C.; Anderson, Derek T.; Aickelin, Uwe

Authors

Shaily Kabir

Christian Wagner

Timothy C. Havens

Derek T. Anderson

Uwe Aickelin



Abstract

In computing the similarity of intervals, current similarity measures such as the commonly used Jaccard and Dice measures are at times not sensitive to changes in the width of intervals, producing equal similarities for substantially different pairs of intervals. To address this, we propose a new similarity measure that uses a bi-directional approach to determine interval similarity. For each direction, the overlapping ratio of the given interval in a pair with the other interval is used as a measure of uni-directional similarity. We show that the proposed measure satisfies all common properties of a similarity measure, while also being invariant in respect to multiplication of the interval endpoints and exhibiting linear growth in respect to linearly increasing overlap. Further, we compare the behavior of the proposed measure with the highly popular Jaccard and Dice similarity measures, highlighting that the proposed approach is more sensitive to changes in interval widths. Finally, we show that the proposed similarity is bounded by the Jaccard and the Dice similarity, thus providing a reliable alternative.

Journal Proceedings of the IEEE International Fuzzy Systems Conference
Electronic ISSN 1544-5615
Peer Reviewed Peer Reviewed
APA6 Citation Kabir, S., Wagner, C., Havens, T. C., Anderson, D. T., & Aickelin, U. (in press). Novel similarity measure for interval-valued data based on overlapping ratio. doi:10.1109/FUZZ-IEEE.2017.8015623
DOI https://doi.org/10.1109/FUZZ-IEEE.2017.8015623
Publisher URL http://ieeexplore.ieee.org/document/8015623/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Published in 2017 Proceedings of IEEE International Fuzzy Systems Conference. IEEE, 2017, isbn: 9781509060344. DOI: 10.1109/FUZZ-IEEE.2017.8015623

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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