An approach to similarity measurement of absence-presence data: the case that common zeros matter

Similarity between objects (documents, persons, answers to a questionnaire, etc.) is generally determined through relations between representations of these objects. In the case of binary representations the presence of a properly (e.g., an index term) carries a weight of one, the absence a weight of zero. In many similarity studies common zeros are ignored. This situation is called the zero insensitive case. In this article, however, we study the zero sensitive case. Clearly, answers to binary questionnaires (yes-no, encoded as 1-0) are zero sensitive, as people who answer 'no' to the same questions are more similar. We present a wish list for such a zero sensitive approach to similarity. Making a difference between common zeros and common ones leads to an 'identitysimilarity' theory. Hence, we move beyond a pure similarity theory. Three approaches to the problem of similarity measurement of presence-absence data, where common zeros matter are presented. In each case a coding approach is used, leading to new representations, which then lead to a similarity ranking. Examples of functions respecting these rankings are given.