Data Perturbation

The foundational technique of adding calibrated random noise to numerical data values. The noise is drawn from a known probability distribution—typically Laplace or Gaussian—with variance tuned to the desired privacy level.

• Mechanism: Original value + random draw from noise distribution
• Key parameter: Scale of noise controls the privacy-utility trade-off
• Example: Adding Laplace(0, 1/ε) noise to a salary column, where ε is the privacy budget
• Preserves: Mean, variance, and covariance structures when properly calibrated

A perturbation method that interchanges sensitive attribute values between records with similar non-sensitive characteristics. Unlike noise addition, swapping maintains the exact marginal distributions of all attributes.

• Mechanism: Select pairs of records with matching quasi-identifiers and exchange their sensitive values
• Controlled by: Swap rate—the percentage of records subjected to exchange
• Preserves: Univariate distributions exactly; multivariate relationships are distorted
• Common use: Census bureaus and statistical agencies for public-use microdata files

The deliberate reduction of data precision by rounding numerical values to a specified base or grouping continuous values into discrete bins. This creates ambiguity about exact values while retaining ordinal relationships.

• Rounding: Replacing 43,287 with 43,000 (base-1000 rounding)
• Coarsening: Converting exact age 34 to age bracket '30-39'
• Top/bottom coding: Capping extreme values (e.g., ages 90+ become '90+')
• Preserves: Rank ordering and broad distributional shape
• Risk: Over-aggressive rounding destroys variance needed for regression analysis

A statistical disclosure control technique that replaces individual values with group averages computed over small clusters of similar records. Each record in a cluster of size k receives the cluster centroid value.

• Process: Partition dataset into groups of k records, compute mean per group, replace each value with its group mean
• Parameter k: Minimum group size—higher k means stronger privacy but greater information loss
• Preserves: Within-group homogeneity is maximized; between-group variance is retained
• Variant: Individual ranking microaggregation applies the technique to each variable independently before multivariate grouping

A probabilistic perturbation technique applied to categorical variables where each category value is randomly transitioned to another category according to a pre-specified Markov transition matrix.

• Mechanism: Define a matrix P where P[i][j] is the probability that true category i is reported as category j
• Key property: The transition matrix is known and can be inverted for unbiased statistical estimation
• Preserves: Expected marginal distributions when the matrix is properly calibrated
• Example: Gender variable with P(male→male)=0.9, P(male→female)=0.08, P(male→missing)=0.02
• Advantage: Allows analysts to correct for perturbation using the known transition probabilities

A constrained data swapping variant where values are exchanged only within a restricted rank range. Unlike unrestricted swapping, this bounds the distortion introduced to any single record.

• Mechanism: Sort records by a continuous variable; swap values only between records whose ranks differ by at most p%
• Parameter p: Maximum rank difference percentage—smaller p means less distortion
• Preserves: Order statistics and rank-based analyses remain largely intact
• Common in: Economic microdata where preserving income ordering is critical for inequality measures
• Trade-off: Tighter rank constraints improve utility but reduce the uncertainty about individual values