A metric for measurable partitions

作者：Mohlin Erik^*

来源：Journal of Mathematical Psychology, 2015, 67: 39-44.

DOI：10.1016/j.jmp.2015.06.003

• Partitions
• Categorization
• Decision trees
• Classification trees
• Clustering
• Colour categorization
• World color survey

Given a set and a measure on it, this note proposes a metric defined on sets of measurable partitions, with countably many cells. For the special case of partitions of a finite set, and the counting measure, the proposed metric coincides with twice the number of pairs of disagreement. For the special case of a probability measure the proposed metric is related to a symmetrized version of conditional information. The proposed metric is applied to the study of natural language colour categorizations: it allows for quantification of the relative importance of universal and culture-specific forces in shaping colour categorizations.

• 出版日期2015-8