Nearest neighbor rules using ordinal information

Focuses on the task of obtaining missing information about some object using nearest-neighbor-type methods. These approaches mediate this problem with the aid of a collection of data objects about which we have full knowledge. These methods require the calculation of the similarity between target and data objects and then the fusion of known values guided by these similarities. We concentrate on a mixed-scale situation: the similarities are numeric values but the missing information is drawn from an ordinal scale. We show that the weighted median provides a fusion operation that can be used in this mixed-scale environment. We look at some classes of nearest-neighbor rules that can be expressed using this framework. Finally, we turn to the problem of learning weighted median-type rules and provide a learning algorithm.