Choosing a Similarity Coefficient for Classification by Binary Variables

Abstract

Pairwise similarity coefficients are popular measure for binary variables. Many different measures of similarity have been proposed in the literature. Then we are interested in which one is the most effective for classifications. We focus on the fact that almost all measures of similarity are composed of interactions and main effects, and conjecture that the most useful similarity is an interaction because main effect don't play a role of classifications but totally order. All combinations of sixteen similarities coefficients and five clustering method were tested with music CD POS data.The cluster validation were assessed by inter-pretable, uniform, reproducible, external and internal criteria. As a result, the similarity coefficient which is more correlative with an interaction turns out more useful for classifications. That is, the best similarity is an interaction.