Exact and Approximate Methods for Data Directed Microaggregation in One or More Dimensions

Microaggregation is a technique for the protection of the confidentiality of respondents in microdata releases. It is used for economic data where respondent identifiability is high. Microaggregation releases the averages of small groups in which no single respondent is dominant. It was developed for univariate data. The data was sorted and the averages of adjacent fixed size groups were reported. The groups can be allowed to have varying sizes so that no group will include a large gap in the sorted data. The groups become more homogeneous when their boundaries are sensitive to the distribution of the data. This is like clustering but with the number of clusters chosen to be as large as possible subject to homogeneous clusters and a minimum cluster size. Approximate methods based on comparisons are developed. Exact methods based on linear optimization are also developed. For bivariate, or higher dimensional, data the notion of adjacency is defined even though sorting is no longer well defined. The constraints for minimum cluster size are also more elaborate and not so easily solved. We may also use only a triangulation to limit the number of adjacencies to be considered in the algorithms. Hybrids of the approximate and exact methods combine the strengths of each strategy.