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

Document Type

Article

Publication Date

8-24-2017

Department

Department of Electrical and Computer Engineering; Center for Data Sciences

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.

Publisher's Statement

©2017 IEEE. Publisher's version of record: https://doi.org/10.1109/FUZZ-IEEE.2017.8015623

Publication Title

2017 IEEE International Conference on Fuzzy Systems

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