Improved Univariate Microaggregation for Integer Values

Privacy issues during data publishing is an increasing concern of involved entities. The problem is addressed in the field of statistical disclosure control with the aim of producing protected datasets that are also useful for interested end users such as government agencies and research communities. The problem of producing useful protected datasets is addressed in multiple computational privacy models such as $k$-anonymity in which data is clustered into groups of at least $k$ members. Microaggregation is a mechanism to realize $k$-anonymity. The objective is to assign records of a dataset to clusters and replace the original values with their associated cluster centers which are the average of assigned values to minimize information loss in terms of the sum of within group squared errors ($SSE$). While the problem is shown to be NP-hard in general, there is an optimal polynomial-time algorithm for univariate datasets. This paper shows that the assignment of the univariate microaggregation algorithm cannot produce optimal partitions for integer observations where the computed centroids have to be integer values. In other words, the integrality constraint on published quantities has to be addressed within the algorithm steps and the optimal partition cannot be attained using only the results of the general solution. Then, an effective method that considers the constraint is proposed and analyzed which can handle very large numerical volumes. Experimental evaluations confirm that the developed algorithm not only produces more useful datasets but also is more efficient in comparison with the general optimal univariate algorithm.