ARX Utility Metrics¶

After each anonymization experiment, ARX — through the RECITALS interface — exposes a set of analysis metrics that characterize the structure and quality of the anonymized dataset. These metrics are retrieved from the ARXResult object returned by RECITALS.

Role¶

While quality models guide the optimizer during anonymization, the ARX utility metrics are read after anonymization to objectively characterize the result: how large are the equivalence classes, how much information was lost per attribute, how many records were suppressed.

flowchart LR
    A[Anonymization\nARX optimizer] --> B[ARXResult\nRECITALS]
    B --> C[Equivalence class metrics]
    B --> D[Per-attribute metrics]
    B --> E[Global structural metrics]
    B --> F[Optimization scores]

Equivalence class metrics¶

Equivalence classes are the groups of records that become indistinguishable from each other on the quasi-identifiers after anonymization.

Metric	Description
Number of equivalence classes	Total count of distinct groups in the anonymized dataset
Average equivalence class size	Mean number of records per group
Minimum equivalence class size	Smallest group (ideally ≥ k)
Maximum equivalence class size	Largest group (large values indicate over-generalization)
Number of suppressed records	Records removed because no valid anonymization was found

A well-anonymized dataset has equivalence classes whose sizes are close to each other (balanced groups) and whose minimum is at least k.

Per-attribute metrics¶

These metrics are computed independently for each quasi-identifier and expose the degree and nature of generalization applied to that attribute.

Granularity¶

Measures the proportion of information preserved for a given attribute after generalization. A value of 1 means no generalization was applied; a value of 0 means the attribute was fully suppressed.

\[\text{granularity}(a) = \frac{\text{preserved information}}{\text{total information in hierarchy}}\]

Non-uniform Entropy¶

Measures the entropy of an attribute's distribution in the anonymized dataset, weighted by the actual frequencies in the original data. Unlike uniform entropy, it accounts for the fact that some values are more common than others.

A higher value indicates greater uncertainty about the original value — i.e., more information loss for that attribute.

Generalization Intensity¶

Measures how deeply values were pushed into the generalization hierarchy for a given attribute. It is expressed as a ratio of the generalization level applied to the maximum height of the hierarchy.

\[\text{intensity}(a) = \frac{\text{applied generalization level}}{\text{max hierarchy height}}\]

0: no generalization (original values kept).
1: full generalization (values suppressed to *).

Attribute-level Squared Error¶

Measures the squared error between original and generalized values for a given attribute, at the attribute level. It quantifies how far the generalized value is from the original, on average.

Global structural metrics¶

Discernibility¶

Penalizes large equivalence classes by computing the sum of the squares of all class sizes.

\[\text{discernibility} = \sum_{G \in \mathcal{G}} |G|^2\]

A lower value is better: it indicates that records are spread across many small, precise groups rather than a few large, vague ones.

Ambiguity¶

Measures the total ambiguity across all records — i.e., the number of original records that each anonymized record could correspond to, summed across the dataset.

SSESST — Sum of Squared Errors for Sensitive attributes¶

Measures the total squared error introduced on sensitive attributes (here income) by the anonymization process. A value of 0 means the sensitive attribute was never altered.

Record-level Squared Error¶

Measures the squared error aggregated at the record level across all attributes. It quantifies the average distortion per record introduced by generalization.

Optimization scores¶

ARX reports the value of the objective function (the chosen quality model) for the transformation it selected.

Score	Description
Minimum optimization score	Best (lowest) information loss found across the search
Maximum optimization score	Worst (highest) information loss found across the search

For multi-attribute quality models (e.g. loss with arithmetic_mean), these scores may be a scalar or a vector depending on the chosen aggregate function.

Summary table¶

Metric	Scope	Provided by
Number of equivalence classes	Global	`get_number_of_equivalence_classes()`
Average equivalence class size	Global	`get_average_equivalence_class_size()`
Min / Max equivalence class size	Global	`get_min/max_equivalence_class_size()`
Number of suppressed records	Global	`get_number_of_suppressed_records()`
Granularity	Per attribute	`get_granularity_metric(attribute)`
Non-uniform entropy	Per attribute	`get_non_uniform_entropy_metric(attribute)`
Generalization intensity	Per attribute	`get_generalization_intensity_metric(attribute)`
Attribute-level squared error	Per attribute	`get_attribute_level_squared_error_metric(attribute)`
Discernibility	Global	`get_discernability_metric()`
Ambiguity	Global	`get_ambiguity_metric()`
SSESST	Global	`get_ssesst_metric()`
Record-level squared error	Global	`get_record_level_squared_error_metric()`
Min / Max optimization score	Global	`get_optimization_score_min/max()`