By Kato Mivule

Noise addition: A stochastic value is added to confidential numeric attributes.

The stochastic value is chosen from a normal distribution with zero mean and a diminutive standard deviation. First publicized by Jay Kim (1986) with the expression that

Z = X + ɛ

Where Z is the transformed data point

X is the original data point.

ɛ (epsilon)is the random variable (noise) with a distribution ε∼ N(0, σ^{2} ).

The X is then replaced with the Z for the data set to be published, Z = X + ɛ
Statistical Considerations in Noise Addition
Gaussian Noise Distribution

The Normal Distribution( Gaussian distribution), is a bell shaped probability distribution depicting realvalued stochastic variables clustered around a single mean…

μ (mu) is the mean

σ^{2} (Sigma) is the variance

N(μ, σ^{2}) is the normal distribution with mean μ and variance σ^{2}
 Transformed data has to keep the same statistical properties as the original data.
 Covariance:Cov(X, Y): How affiliated the deviations between points X and Y.
 If Cov(X, Y) is positive, X and Y increase together, otherwise they don’t.
 If Cov(X, Y) is zero, X and Y are each autonomous.
 Correlation r_{xy} calculates tendency of linear relation between two data points.
 If 1, then r_{xy} is a negative linear relation between x and y,
 if 0, no linear relation,
 if +1, a strong linear relation.
Notes
[1] Jay Kim, A Method For Limiting Disclosure in Microdata Based Random Noise and Transformation, Proceedings of the Survey Research Methods, American Statistical Association, Pages 370374, 1986.
[2] J. Domingoferrer, F. Sebe, and J. CastellaRoca, “On the security of noise addition for privacy in statistical databases,” in Privacy in Statistical Databases 2004, 2004, pp. 149161. [Online]. Available: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.4575
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