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We are working with personally identifiable information that needs to be de-identified. Is there an existing hierarchy or taxonomy of different kinds of re-identification properties?

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I don't know of formal work. Generally information is re-correlated from components by two heuristic activities: aggregation and inference. Aggregation is the collection of small components of a larger piece of information with the goal of collecting all the pieces. Inference is the collection of information fragments or related information with the goal of deducing or inducing the target information. Aggregation is frustrated by minimal size fragmentation and high dispersion. Inference is frustrated by noise, set mixing, and self-referential data.

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