Is unicity always reported for four points?

No. The number of observations is part of the test design.

Does deleting names guarantee low unicity?

No. Other combinations can remain distinctive.

Does coarsening always make data safe?

No. It can reduce uniqueness under a specified test without establishing comprehensive protection.

AI Glossary / Data science and analytics / Advanced

Unicity (data analysis)

Definition

Unicity measures how often a limited set of observations singles out one individual's record or trace within a dataset. In privacy research, it is commonly expressed as the fraction of tested traces uniquely matched by a specified number of known points. Its value depends on the data, observation-selection procedure and matching resolution.

What it means

Removing names does not necessarily make behavioral records indistinguishable. A combination of otherwise ordinary observations can occur in only one trace. Unicity examines this distinctiveness under a defined test.
The concept is particularly associated with research on longitudinal data, where each person contributes a sequence of observations. The question is not merely whether two full records are identical. It is whether a small amount of information is sufficient to isolate one trace among the candidates.
A unique match within a dataset is not automatically a verified real-world identity. Identification also depends on whether relevant outside information is available, accurate and linkable to a person. Keep the uniqueness measurement separate from claims that actual people have been identified.

How it works

Specify the dataset, the unit represented by each trace and the number of observations to be used in the test. Define how those observations are selected and what counts as a match. Time and location resolution, missing data and measurement error can change the answer.
For each selected trace, take observations according to the stated procedure and count the dataset traces compatible with all of them. If exactly one trace matches, the test records a unique outcome. The proportion of unique outcomes across the evaluation gives the estimated unicity for that procedure.
Repeat or vary the procedure to examine its sensitivity. A result based on randomly selected observations is not interchangeable with one based on deliberately selecting the rarest observations. Likewise, uniqueness in a small sample should not silently be described as uniqueness in the entire population.

Three practical examples

1. Research sharing: A team assesses whether a proposed pseudonymous activity dataset contains distinctive combinations before deciding what information should be made available to collaborators.
2. Product analytics: An organization compares uniqueness under hourly and daily time bins, alongside the usefulness of each version for its intended analysis.
3. Training: Learners examine fictional records to understand why replacing names with random identifiers does not necessarily remove the information that distinguishes records.
These examples concern assessment and education, not attempts to identify particular real people.

Think of it this way

Think of a library catalog in which book titles are hidden. A few descriptive details may still match only one book. That establishes uniqueness within the catalog under those details. Connecting that entry to a title requires additional information. The two steps are related, but they are not the same claim.

Worked example

Consider five entirely fictional activity traces, each with one morning and one afternoon category. The pairs are A = Reading - Video, B = Reading - Audio, C = Exercise - Video, D = Exercise - Audio and E = Reading - Video.
Use a fixed test that reveals both categories for every trace. B, C and D each have a pair found only once. A and E share their pair. Three of the five traces are unique, giving 3 / 5 = 60% unicity for this test.
If the test reveals only the morning category, Reading matches three traces and Exercise matches two. None is unique, so the measured fraction is 0%.
If the afternoon categories are both merged into Media, the two-category test also produces no unique traces. This particular transformation removes the distinction that made B, C and D unique.
The calculation is not a general privacy guarantee. It uses a tiny invented dataset, fixed observation positions and exact matching. Different additional attributes or a different candidate dataset could produce different results.

Illustrative case study

Fictional education researcher Cedar Insights prepares session records for a collaboration. Direct identifiers have been replaced, but the team recognizes that detailed activity histories can remain distinctive.
Before release, analysts conduct an authorized internal assessment using documented observation rules. They compare versions with different time detail and review how the changes affect the research questions. They also consider whether person-level records are needed at all, rather than assuming the most detailed file is the default deliverable.
Cedar treats the uniqueness results as one input to its disclosure assessment, alongside access arrangements and other potential information. It does not label a dataset anonymous solely because one chosen unicity test gives a low value. This is a fictional decision process, not a reported deployment or assurance claim.

Common misconceptions and mistakes

Unicity is not simply a count of duplicate full rows. Partial observations across a person's trace are central to the question.
A percentage without the observation count and selection rule is incomplete. The same data can yield different measurements under different tests.
The famous results from a particular mobility study are not universal constants. They depend on the studied data and resolution.
A low measured value does not prove the absence of all disclosure risks. Other attributes, external information or inference methods may matter.
A unique trace does not by itself supply a person's name. Avoid presenting distinctiveness as completed identity verification.

Business use

Unicity can help data owners evaluate the distinctiveness of proposed datasets and compare release designs. Document the assessment population, matching assumptions and transformations so the result is interpretable. Balance analytical usefulness with the information actually required for the project. Any decision to share personal-level data needs a broader assessment than a single uniqueness percentage, particularly when future auxiliary information is uncertain.

Check your understanding

Why are A and E not unique in the example?

Answer: Their observed category pairs match.

Why is the measured fraction 60%?

Answer: Three of five traces have unique pairs under the fixed test.

Why report the selection rule?

Answer: Different known observations can lead to different candidate matches.

Related terms

Anonymization
Longitudinal data
Re-identification risk
pseudonymisation
quasi-identifier
data minimisation
disclosure control
privacy assessment

Learn next

Using fictional data, compare uniqueness under two observation rules and two levels of aggregation. Explain exactly what each result establishes and which privacy questions remain outside the test.

Sources

Yves-Alexandre de Montjoye, César A. Hidalgo, Michel Verleysen and Vincent D. Blondel, Unique in the Crowd: The Privacy Bounds of Human Mobility, Scientific Reports, 2013. Author-hosted full paper: https://perso.uclouvain.be/michel.verleysen/papers/scientificreports13yadm.pdf The paper supplies the research context and matching-based unicity concept. The five-trace calculation and Cedar Insights case are original illustrations; they are not measurements from its mobility dataset.

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