Hypermatching: Similarity Matching With Extreme Values

An approach is developed for object similarity to support a focus on the role of extreme values in object matching, which is termed hypermatching. Importance weights are first introduced to the matching and variations formulated for objects that do not share all the same attributes. Extreme attribute values are considered by introducing amplification of attribute importance and several significant cases examined. The objects can both possess the same or different extreme valued attributes. Another case is where one object may have an extreme attribute, which the other object does not have. Then, the analysis of the effect of multiple extreme attributes is presented. Finally for attributes with 0-1 values (features), similarity matching is considered and a closed form solution for the similarity is developed. This provides the basis for the Yager-Petry index, which is then compared with the Jaccard similarity index.