Comparing proximity measures for continuous and binary data: topological approach
Résumé
In many application domains, the choice of a proximity measure directly affects the resulting data mining methods in the clustering, comparison or structuring of a set of objects. Generally, the user is obliged to choose one proximity measure among many existing ones. According to the notion of equivalence, like the one based on pre-ordering, some of the proximity measures are more or less equivalent, which means that they produce, more or less, the same results. In this paper, we introduce a new approach to comparing proximity measures. This approach is based on topological equivalence which exploits the concept of local neighbors. It defines equivalence between two proximity measures as having the same neighborhood structure on the objects. We illustrate our approach upon thirty-six proximity measures used with continuous and binary attributes.
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