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Privacy Preserving Market Basket Data Analysis

Privacy Preserving Market Basket Data Analysis. Ling Guo, Songtao Guo, Xintao Wu University of North Carolina at Charlotte. Market Basket Data. …. 1: presence 0: absence. Association rule (R.Agrawal SIGMOD 1993) with support and confidence .

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Privacy Preserving Market Basket Data Analysis

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  1. Privacy Preserving Market Basket Data Analysis Ling Guo, Songtao Guo, Xintao Wu University of North Carolina at Charlotte

  2. Market Basket Data … 1: presence 0: absence • Association rule (R.Agrawal SIGMOD 1993) • with support and confidence

  3. Other measures 2 x 2 contingency table Objective measures for A=>B

  4. Related Work • Privacy preserving association rule mining • Data swapping • Frequent itemset or rule hiding • Inverse frequent itemset mining • Item randomization

  5. Item Randomization Original Data Randomized Data • To what extent randomization affects mining results? (Focus) • To what extent it protects privacy?

  6. Randomized Response ([ Stanley Warner; JASA 1965]) : Cheated in the exam : Didn’t cheat in the exam Cheated in exam Purpose Purpose: Get the proportion( ) of population members that cheated in the exam. • Procedure: “Yes” answer Didn’t cheat Randomization device Do you belong to A? (p) Do you belong to ?(1-p) … … “No” answer As: Unbiased estimate of is:

  7. Application of RR in MBD • RR can be expressed by matrix as: ( 0: No 1:Yes) = • Extension to multiple variables e.g., for 2 variables • Unbiased estimate of is: stands for Kronecker product diagonal matrix with elements

  8. Randomization example Original Data Randomized Data RR A: Milk B: Cereals Data owners Data miners =(0.368,0.097,0.218,0.316)’ =(0.415,0.043,0.183,0.359)’ =(0.427,0.031,0.181,0.362)’ 0.671 0.662 We can get the estimate, how accurate we can achieve?

  9. Motivation Estimated values Both are frequent set Original values Frequent set 36.3 Not frequent set 35.9 31.5 Rule 6 is falsely recognized from estimated value! 22.1 23.8 12.3 Lower& Upper bound Frequent set with high confidence Frequent set without confidence

  10. Accuracy on Support S • Estimate of support • Variance of support • Interquantile range (normal dist.) 0.362 0.346 0.378

  11. Accuracy on Confidence C • Estimate of confidence A =>B • Variance of confidence • Interquantile range (ratio dist. is F(w)) • Loose range derived on Chebyshev’s theorem where Let be a random variable with expected value and finite variance .Then for any real

  12. Bounds of other measures Accuracy Bounds

  13. General Framework • Step1: Estimation • Express the measure as one derived function from the observed variables ( or their marginal totals , ). • Compute the estimated measure value. • Step2: Variance of the estimated measure • Get the variance of the estimated measure (a function with multi known variables) through Taylor approximation • Step 3: Derive the interquantile range through Chebyshev's theorem

  14. Example for with two variables • Step 1: Get the estimate of the measure • Step 2: Get the variance of the estimated measure • Step 3: Derive the interquantile range through Chebyshev's theorem . Where: , , ,

  15. Accuracy Bounds • With unknown distribution, Chebyshev theorm only gives loose bounds. Bounds of the support vs. varying p

  16. Distortion • All the above discussions assume distortion matrices P are known to data miners • P could be exploited by attackers to improve the posteriori probability of their prediction on sensitive items • How about not releasing P? • Disclosure risk is decreased • Data mining result?

  17. Unknown distortion P • Some measures have monotonic properties • Other measures don’t have such properties

  18. Applications: hypothesis test • From the randomized data, if we discover an itemset which satisfies , we can guarantee dependence exists among the original itemset since . Still be able to derive the strong dependent itemsets from the randomized data No false positive

  19. Conclusion • Propose a general approach to deriving accuracy bounds of various measures adopted in MBD analysis • Prove some measures have monotonic property and some data mining tasks can be conducted directly on randomized data (without knowing the distortion). No false positive pattern exists in the mining result.

  20. Future Work • Which measures are more sensible to randomization? • The tradeoff between the privacy of individual data and the accuracy of data mining results • Accuracy vs. disclosure analysis for general categorical data

  21. Acknowledgement • NSF IIS-0546027 • Ph.D. students Ling Guo Songtao Guo

  22. Q A &

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