On Optimizing the k-Ward Micro-aggregation Technique for Secure Statistical Databases

Abstract

We consider the problem of securing a statistical database by utilizing the well-known micro-aggregation strategy, and in particular, the k-Ward strategy introduced in [1] and utilized in [2]. The latter scheme, which represents the state-of-the-art, coalesces the sorted data attribute values into groups, and on being queried, reports the means of the corresponding groups. We demonstrate that such a scheme can be optimized on two fronts. First of all, we minimize the computations done in evaluating the between-class distance matrix, to require only a constant number of updating distance computations. Secondly, and more importantly, we propose that the data set be partitioned recursively before a k-Ward strategy is invoked, and that the latter be invoked on the “primitive” sub-groups which terminate the recursion. Our experimental results, done on two benchmark data sets, demonstrate a marked improvement. While the information loss is comparable to the k-Ward micro-aggregation technique proposed by Domingo-Ferrer et.al. [2], the computations required to achieve this loss is a fraction of the computations required in the latter – providing a computational advantage which sometimes exceeds 80% if one method is used by itself, and more than 90% if both enhancements are invoked simultaneously.