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The metric‐frequency measure of similarity for ill‐structured data sets, with an application to family therapy
Author(s) -
Sales Célia M. D.,
Wakker Peter P.
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x376070
Subject(s) - nomothetic and idiographic , measure (data warehouse) , metric (unit) , similarity (geometry) , set (abstract data type) , similarity measure , computer science , data set , feature (linguistics) , mathematics , data mining , artificial intelligence , theoretical computer science , psychology , social psychology , linguistics , operations management , philosophy , economics , image (mathematics) , programming language
Similarity measures have been studied extensively in many domains, but usually with well‐structured data sets. In many psychological applications, however, such data sets are not available. It often cannot even be predicted how many items will be observed, or what exactly they will entail. This paper introduces a similarity measure, called the metric‐frequency (MF) measure, that can be applied to such data sets. If it is not known beforehand how many items will be observed, then the number of items actually observed in itself carries information. A typical feature of the MF is that it incorporates such information. The primary purpose of our measure is that it should be pragmatic, widely applicable, and tractable, even if data are complex. The MF generalizes Tversky's set‐theoretic measure of similarity to cases where items may be present or absent and at the same time can be numerical as with Shepard's metric measure, but need not be so. As an illustration, we apply the MF to family therapy where it cannot be predicted what issues the clients will raise in therapy sessions. The MF is flexible enough to be applicable to idiographic data.