How to compare uncertain data types: towards robust similarity measures - Kabir, Shaily (2020)
In view of the importance of effective comparison of uncertain data in real-world applications, this thesis focuses on developing new similarity measures with high accuracy. As it identifies and articulates an inherent limitation of the popular set-theoretic similarity measures for continuous intervals where they return the same similarity value for very different sets of intervals (termed as aliasing), this thesis first underpins a new axiomatic definition of a robust similarity measure and then proposes a new similarity measure for continuous intervals based on their bidirectional subsethood. Beyond establishing theoretical foundation of the new measure, the thesis also demonstrates its robust results vis-a-vis existing measures and suitability for real world applications. In the next stage, it develops a generalized framework to assess similarity between discontinuous intervals as current approaches involve loss of discontinuity information and are also affected by aliasing of the popular measures— these weaknesses impact the accuracy of similarity results. This thesis further integrates Allen’s theory with the new generalized framework to make the latter more efficient.