A measure of variance for hierarchical nominal attributes
The need for measuring the dispersion of nominal categorical attributes appears in several applications, like clustering or data anonymization. For a nominal attribute whose categories can be hierarchically classified, a measure of the variance of a sample drawn from that attribute is proposed which takes the attributes hierarchy into account. The new measure is the reciprocal of consanguinity: the less related the nominal categories in the sample, the higher the measured variance. For non-hierarchical nominal attributes, the proposed measure yields results consistent with previous diversity indicators. Applications of the new nominal variance measure to economic diversity measurement and data anonymization are also discussed.
variance nominal attributes clustering data anonymization diversity spread categorical hierarchy data privacy