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Quality Models

Quality models are objective functions that ARX minimizes when searching for the optimal transformation. They quantify the information loss caused by generalization and suppression.

Role

During anonymization, ARX explores the space of possible transformations and selects the one that satisfies the privacy constraints while minimizing the loss measured by the chosen quality model.

The choice of quality model directly influences which transformation ARX considers "the best".

Available quality models

loss — Information Loss (default)

Measures the overall information loss caused by generalization. For each attribute, it computes the ratio between the size of the generalized group and the total size of the hierarchy.

height — Hierarchy Height

Measures the average generalization level applied within the hierarchies. A high level means that values have been strongly generalized (pushed high up in the generalization tree).

  • Favors transformations that stay close to the original values.
  • Compatible with aggregate functions.

precision — Precision

Measures the granularity of values retained in the anonymized dataset. High precision indicates that values have only been slightly generalized.

\[\text{precision}(a) = 1 - \frac{\text{generalization level}}{\text{maximum hierarchy height}}\]

nm_entropy — Non-uniform Entropy

Measures the entropy of attribute distributions while accounting for the actual frequencies of values. Unlike classical entropy, it weights each value by its frequency in the original data.

  • More sensitive to distribution imbalances than classical entropy.
  • Compatible with aggregate functions.

entropy — Entropy

Measures the information-theoretic entropy of the anonymized dataset. It quantifies the uncertainty introduced by generalization.

  • Not compatible with aggregate functions.

discernibility — Discernibility

Penalizes large equivalence classes. It computes the sum of the squares of all equivalence class sizes.

\[\text{discernibility} = \sum_{G \in \mathcal{G}} |G|^2\]
  • A lower value indicates smaller groups and therefore better data precision.
  • Not compatible with aggregate functions.

aecs — Average Equivalence Class Size

Measures the average size of equivalence classes in the anonymized dataset.

\[\text{AECS} = \frac{n}{\text{number of equivalence classes}}\]
  • A simple indicator of anonymization granularity.
  • Not compatible with aggregate functions.

ambiguity — Ambiguity

Measures the degree of ambiguity of each record — i.e., the number of possible values for each attribute after generalization.

  • Not compatible with aggregate functions.

classification — Classification Metric

Utility metric oriented towards preserving utility for supervised classification tasks.

  • Not compatible with aggregate functions.

Summary

Model Short description Aggregate supported
loss Overall information loss ✓
height Generalization depth ✓
precision Preserved granularity ✓
nm_entropy Frequency-weighted entropy ✓
entropy Information-theoretic entropy ✗
discernibility Sum of squared group sizes ✗
aecs Average equivalence class size ✗
ambiguity Record ambiguity level ✗
classification Classification utility ✗

Configuration

The quality model is specified in the JSON configuration file of each experiment:

{
  "utility_measure": "loss",
  "utility_aggregate": "arithmetic_mean"
}

The default value is loss with the arithmetic_mean aggregate.