privacy preservation for data streams

Privacy Preservation for Data StreamsFeifei Li, Boston University

Joint work with:Jimeng Sun (CMU), Spiros Papadimitriou, George A. Mihaila and Ioana Stanoi (IBM T.J. Watson Research Center)

Privacy Preservation for Data StreamsPrivacy Preservation for Data Streams

2

Application (1)

Corp. A

Corp. B

Corp. C

Analytical Services

Finding trends, clusters, patterns,

aggregations.Sensitive data

P

P

P


3

Application (2)

Corp. A Information Hub

Publish data as a service

Client A

Client B

Subscribe data to identify trends, patterns, classes

P


4

Target Application Identify trendsvalue

timevalue

timevalue

timevalue

time

stream 1

stream 2

stream 3

stream 4

Cluster/classificati

on


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Problem Formulation

time

time

time

……

..

A1

A2

AN

t

A1t

),1[, TA NT

Nt RA

+ NTE *NTA

Online generated noise,

one vector at a time


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Problem Formulation (continued)

time

time

time

……

.

*NTA Rx

~NTA

),(min ~NTNTR AAD Offline and

Online

Given σ2, obtain A* online, s.t. D(A, A*) = σ2, and for given R, D(A, A~) is close to σ2


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Data Perturbation

time

time

time

time

time

time

time

time

+

Random i.i.d noise

i.i.d: identical independently distributed


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Principal Component Analysis: PCA

i.i.d Noise


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Principal Component Analysis: PCA

Correlated Noise


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PCA Based Data Reconstruction

A

A~

Removed Noise

Principal Direction

Remaining Noise

Privacy

A*

σ2

Added Noise: Utility

Projection Error

A*: Perturbed Data

A: Original Data

A~: Reconstructed Data


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PCA Based Data Reconstruction

A

A~ Principal Direction

Remaining Noise

Privacy

A*σ2

Added Noise: Utility

Projection Error

A*: Perturbed Data

A: Original Data

A~: Reconstructed DataCorrelated Noise!


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Data Perturbation: main idea

Observations

–The amount of the random noise controls privacy/utility tradeoff

– i.i.d (identical independently distributed) noise does not preserve the privacy! Not well enough

Lesson learned

– Noise should be correlated with original data

• Z. Huang et al. Sigmod 05.


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Challenge 1: Dynamic Correlation


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Challenge 1: Dynamic Correlation


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Challenge 2: Dynamic Autocorrelation


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Challenge 2: Dynamic Autocorrelation


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Online Random Noise for Autocorrelation: Stock


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State of the Art

Privacy Preservation

–Given a utility requirement, maximize the privacy

Existing Work (Z. Huang et al. Sigmod05)

–Batch mode, static data

–And many other works (see our paper for a detailed literature review)


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Adding Dynamic Correlated Noise

A1

A2

A3

+

U3x3: online estimation

of principal components

At

Update U

Et

Generate noisedistributed along U

A~t

Publish A~

t

S. Papadimitriou et al. VLDB05


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Put it into Algorithm: Distribute Noise

V

V )1(1 2

V

V )2(2 2

σ2 σ2

TU

k=3, U: eigenvectors, V: eigenvalues

Added to AtRotate back to data space

Noise distributed in principal components’ subspace


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why is our algorithm better (state of the art)?

Local principal component Local principal

component

Global principal component

Noise added along global PC -- offline

Removed noise by online reconstruction

Noise added along global PC -- offline

Removed noise by online reconstruction


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Online Reconstruction vs. Offline Reconstruction

Choice of adversary:

– Offline reconstruction based on global principal components

– Online tracking of the principal components and apply local reconstruction

– Please see the details in the paper


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Tracking Autocorrelation

a=[1 2 3 4 5 6]T

w1

w2

w3

w4

W =

1 2 3

2 3 4

3 4 5

4 5 6

Time

h streams


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Distribute Noise

W =

1 2 3

2 3 4

3 4 5

4 5 6

1 2 3

2 3 4

3 4 5

4 5 6

1 2 3

2 3 4

3 4 5

4 5 6

1 2 3

2 3 4

3 4 5

4 5 6

1 2 3

2 3 4

3 4 5

4 5 6

Avoid adding noise > allowed threshold!

And still auto-correlated with the stream Idea: constraint the

next k noise values based on previous h-k noises + current estimation of U becomes a linear system


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Experiments

Three Real Data Streams

– Sensor streams, Lab: Light, Humidity, Volt, Temperature. 7712x198

– Choroline environmental streams: 4310x166

– Stock streams: 8000x2


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Perturbation vs. Reconstruction

Perturbation i.i.d-N Offline-N Online-N: SCAN / SACAN

Reconstruction

Baseline Offline-R Online-R: SCOR / SACOR

noise correlated with global principal componentsstreaming correlated additive noisestreaming auto-correlated additive noiseoffline-reconstruction based on global principal componentsstreaming correlated online reconstructionstreaming auto-correlated online reconstruction

noise (discrepancy) is represented by the relative energy as percentage to the original data streams,i.e., D(A, A*)/||A||

take perturbed data as the reconstruction


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Reconstruction Error: Online-R vs. Offline-R

online reconstruction achieves better accuracy asit minimizes the projection error

10% noisek=10


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Reconstruction Error: vary k

1. online reconstruction achieves better accuracy2. large k reduces projection error


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Privacy vs. Discrepancy, online-R: Lab data


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Privacy vs. Discrepancy, online-R: Choroline


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Online Random Noise for Autocorrelation: Choroline


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Online Random Noise for Autocorrelation: Stock


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Privacy vs. Discrepancy: Online-R (Choroline)


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Privacy vs. Discrepancy: Online-R (Stock)


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Running Time Analysis


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Running Time Analysis


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Future Work

Combing correlation and autocorrelation

Other type of data streams, other than numeric data, such as categorical data


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Questions

Thank you!

privacy preservation for data streams

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