Comparing L 1 and L 2 Distances for CTA

Abstract

Minimum distance controlled tabular adjustment (CTA) is a recent perturbative technique of statistical disclosure control for tabular data. Given a table to be protected, CTA looks for the closest safe table, using some particular distance. We focus on the continuous formulation of CTA, without binary variables, which results in a convex optimization problem for distances L 1, L 2 and L ∞ . We also introduce the L 0-CTA problem, which results in a combinatorial optimization problem. The two more practical approaches, L 1-CTA (linear optimization problem) and L 2-CTA (quadratic optimization problem) are empirically compared on a set of public domain instances. The results show that, depending on the criteria considered, each of them is a better option.Keywordsstatistical disclosure controlcontrolled tabular adjustmentlinear optimizationquadratic optimization