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

Microaggregation is a technique used for the protection of the confidentiality of respondents in microdata releases. It is typically used for economic data where respondent identifiability is quite high. Rather than releasing a perturbed version of the data, microaggregation releases the averages of small groups in which no single respondent is dominant. The original form of microaggregation was for univariate data. It was implemented by sorting the data and then reporting the averages of adjacent groups of fixed size. Any partial group at the end would be pooled with the final complete group to ensure that the desired minimum group size was obtained. The typical group size was small, with five a common choice. An immediate improvement would be to allow some number of internal groups, perhaps near the center of the data, to be larger to compensate for the incomplete group. As a further improvement the groups can be allowed to have varying sizes so that no group will include a large gap in the sorted data. Each of the resulting groups can be more homogeneous when the group boundaries are allowed to be sensitive to the distribution of the data. This can be described as a clustering problem with a variable number of clusters and a minimum cluster size. The number of clusters is chosen to be as large as possible consistent with homogeneous clusters and the minimum cluster size. Techniques for determining such data directed microaggregations have been proposed which use randomized searching methods. These methods are typically terminated early as they are quite expensive to operate. They seek to minimize the total within cluster sum of squares as suggested by some clustering methods. They have two disadvantages of not leading to readily solved optimization problems and of not being the most suitable criterion for highly skewed data typical of economic applications. For highly skewed data the width of the clusters may be a more suitable measure. The total within cluster width may be obtained by summing the gaps between adjacent members of the clusters. Cluster size may be controlled by requiring a minimum number of adjacent gaps be included in any cluster. The result is an optimization problem for a linear objective function over the indicator variables for the gap inclusions. Each data point and its potential cluster neighbors would appear in a constraint which enforces the minimum cluster size. The resulting system can be readily