Concept Dissimilarity based on Tree Edit Distance and Morphological Dilation
Felix Distel, J. Atif, Isabelle Bloch · HAL (Le Centre pour la Communication Scientifique Directe) · 2014
Several researchers have developed properties that ensure compatibility of a concept similarityor dissimilarity measure with the formal semantics of Description Logics. While these authors havehighlighted the relevance of the triangle inequality, none of their proposed dissimilarity measuressatisfy it. In this work we present several dissimilarity measures with this property: first, a simpledissimilarity measure, based on description trees for the lightweight Description LogicEL; second, ageneral framework based on concept relaxations; third, an instantiation of the general framework usingdilation operators from mathematical morphology, exploiting the link between Hausdorff distanceand dilations using balls of the ground distance as structuring elements. A comparison between thesedefinitions and their properties is provided as well.