Comparing L1 and L2 distances for CTA

  • Authors:
  • Jordi Castro

  • Affiliations:
  • Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Barcelona, Catalonia, Spain

  • Venue:
  • PSD'12 Proceedings of the 2012 international conference on Privacy in Statistical Databases
  • Year:
  • 2012

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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 L1, L2 and L∞. We also introduce the L0-CTA problem, which results in a combinatorial optimization problem. The two more practical approaches, L1-CTA (linear optimization problem) and L2-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.