Similarity of Attributes by External Probes

Gautam Das, Heikki Mannila and Pirjo Ronkainen

In data mining, similarity or distance between attributes is one of the central notions. Such a notion can be used to build attribute hierarchies etc. Similarity metrics can be user-defined, but an important problem is defining similarity on the basis of data. Several methods based on statistical techniques exist. For defining the similarity between two attributes A and B they typically consider only the values of A and B, not the other attributes. We describe how a similarity notion between attributes can be defined by considering the values of other attributes. The basic idea is that in a 0/1 relation r, two attributes A and B are similar if the subrelations \sigma_{A=1}(r) and \sigma_{B=1}(r) are similar. Similarity between the two relations is defined by considering the marginal frequencies of a selected subset of other attributes. We show that the framework produces natural notions of similarity. Empirical results on the Reuters-21578 document dataset show, for example, how natural classifications for countries can be discovered from keyword distributions in documents. The similarity notion is easily computable with scalable algorithms.


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