Privacy-Preserving Data Mining

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Privacy-Preserving Data Mining

• Representor Li Cao
• October 15, 2003

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Presentation organization

• Associate Data Mining with Privacy
• Privacy Preserving Data Mining scheme using
  random perturbation
• Privacy Preserving Data Mining using Randomized
  Response Techniques
• Comparing these two cases

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Privacy protection historyPrivacy concerns
nowadays

• Citizens attitude
• Scholars attitude

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Internet users attitudes
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Privacy value

• Filtering to weed out unwanted information
• Better search results with less effort
• Useful recommendations
• Market trend
• Example
• From the analysis of a large number of
  purchase transaction records with the costumers
  age and income, we know what kind of costumers
  like some style or brand.

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Motivation (Introducing Data Mining )

• Data Minings goal discover knowledge, trends,
  patterns from large amounts of data.
• Data Minings primary task developing accurate
  models about aggregated data without access to
  precise information in individual data records.
  (Not only discovering knowledge but also
  preserving privacy)

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Presentation organization

• Associate Data Mining with Privacy
• Privacy Preserving Data Mining scheme using
  random perturbation
• Privacy Preserving Data Mining using Randomized
  Response Techniques
• Comparing these two cases

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Privacy Preserving Data Mining scheme using
random perturbation

• Basic idea
• Reconstruction procedure
• Decision-Tree classification
• Three different algorithms

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Attribute list of a example
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Records of a example
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Privacy preserving methods

• Value-class Membership the values for an
  attribute are partitioned into a set of disjoint,
  mutually-exclusive classes.
• Value Distortion xir instead of xi where r is
  a random value.
• a) Uniform
• b) Gaussian

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Basic idea

• Original data ? Perturbed data (Let users provide
  a modified value for sensitive attributes)
• Estimate the distribution of original data from
  perturbed data
• Build classifiers by using these reconstructed
  distributions (Decision-tree)

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Basic Steps
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Reconstruction problem

1. View the n original data value x1,x2,xn of a
   one-dimensional distribution as realizations of n
   independent identically distributed (iid) random
   variables X1,X2,Xn, each with the same
   distribution as the random variable X.
2. To hide these data values, n independent random
   variables Y1,Y2Yn have been used, each with the
   same distribution as a different random variable
   Y.

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• Given x1y1, x2y2xnyn (where yi is the
  realization of Yi) and the cumulative
  distribution function Fy for Y, we would like to
  estimate the cumulative distribution function Fx
  for X.
• In short, given a cumulative distribution Fy and
  the realizations of n iid random samples X1Y1,
  X2Y2,XnYn, estimate Fx.

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Reconstruction process

• Let the value of XiYi be wi (xiyi). Use Bayes
  rule to estimate the posterior distribution
  function Fx1 (given that X1Y1w1) for X1,
  assuming we know the density function fx and fy
  for X and Y respectively.

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• To estimate the posterior distribution function
  Fx given x1y1, x2y2xnyn, we average the
  distribution function for each of the Xi.

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• The corresponding posterior density function, fx
  is obtained by differentiating Fx
• Given a sufficiently large number of samples, fx
  will be very close to the real density function
  fx.

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Reconstruction algorithm

• fx0 Uniform distribution
• j 0 //Iteration number
• Repeat
• j j1
• until (stopping criterion met)

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Stopping Criterion

• Observed randomized distribution ? The result of
  randomizing the current estimate of the original
  distribution
• The difference between successive estimates of
  the original distribution is very small.

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Reconstruction effect
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Decision-Tree Classification

• Tow stages
• (1) Growth (2) Prune
• Example

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Tree-growth phase algorithm

• Partition (Data S)
• begin
• if (most points in S are of the same
  class)
• then return
• for each attribute A do
• evaluate splits on attribute A
• Use best split to partition S into S1
  and S2
• Partition (S1)
• Partition (S2)
• end

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Choose the best split

• Information gain (categorical attributes)
• Gini index (continuous attributes)

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Gini index calculation

• (pj is the relative frequency of class j in
  S)
• If a split divides S into two subsets S1 and S2
• Note Calculating this index requires only
  the distribution of the class values.

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When How original distribution are reconstructed

• Global Reconstruct the distribution for each
  attribute once. Decision-tree classification.
• ByClass For each attribute, first split the
  training data by class, then reconstruct the
  distributions separately. Decision-tree
  classification
• Local The same as in ByClass, however, instead
  of doing reconstruction only once, reconstruction
  is done at each node.

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Example (ByClass and Local)
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Comparing the three algorithms
Execution Time Accuracy
Global Cheapest Worst
ByClass Middle Middle
Local Most expensive Best
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Presentation Organization

• Associate Data Mining with Privacy
• Privacy Preserving Data Mining scheme using
  random perturbation
• Privacy Preserving Data Mining using Randomized
  Response Techniques
• Comparing these two cases
• Are there any other classification methods
  available?

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Privacy Preserving Data Mining using Randomized
Response Techniques

• Randomized Response
• Building Decision-Tree
• Key Information Gain Calculation
• Experimental results

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Randomized Response

• A survey contains a sensitive attribute A.
• Instead of asking whether the respondent has the
  attribute A, ask two related questions, the
  answer to which are opposite to each other (have
  A ? no A).
• Respondent use a randomizing device to decide
  which question to answer. The device is designed
  in such way that the probability of choosing the
  first question is ? .

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• To estimate the percentage of people who has the
  attribute A, we can use
• P(Ayes) P(Ayes) ? P(Ano)(1- ?)
• P(Ano) P(Ano) ? P(Ayes)(1- ?)
• P(kyes) The proportion of the yes
  responses obtained from the survey data.
• P(kyes) The estimated proportion of the
  yes responses
• Our Goal P(Ayes) and P(Ano)

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Example

• Sensitive attribute Married?
• Two questions
• A? Yes / No
• B? No / Yes

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Decision-Tree (Key Info Gain)

• m m classes assumed
• Qj The relative frequency of class j in S
• v any possible value of attribute A
• Sv The subset of S for which attribute A has
  value v.
• Sv The number of elements in Sv
• S The number of elements in S

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• P(E) The proportion of the records in the
  undisguised data set that satisfy Etrue
• P(E) The proportion of the records in the
  disguised data set that satisfy Etrue
• Assume the class label is binary.
• So the Entropy(S) can be calculated.
  Similarly, calculate Sv. At last, we get
  Gain(S,A).

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Experimental results
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Comparing these two cases
Perturbation Response
Attribute Continuous Categorical
Privacy Preserving method Value distortion Randomized response
Choose attribute to split Gini index Information Gain
Inverse procedure Reconstruct distribution Estimate P(E) from P(E)
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Future work

• Solve categorical problems by the first scheme
• Solve continuous problems by the second scheme
• Combine these two scheme to solve some problems
• Other classification suitable