Vertically Partitioned Data
Data is said to be vertically partitioned when several organizations own different attributes of information for the same set of entities. Thus, vertical partitioning of data can formally be defined as follows: First, define a dataset D in terms of the entities for whom the data are collected and the information that is collected for each entity. Thus, D ≡ (E, I), where E is the entity set for whom information is collected and I is the feature set that is collected. Assume that there are k different sites, P1,...,Pk collecting datasets D1 ≡ (E1, I1),...,Dk ≡ (Ek, Ik) respectively. Therefore, data is said to be vertically partitioned if E = ⋂iEi = E1 ⋂...⋂ Ek, and I = ⋃iIi = I1 ⋃...⋃ Ik. In general, distributed data can be arbitrarily partitioned. Vertical partitioning can also be defined as a special case of arbitrary partitioning, where all of the partitions consist of information about the same set of entities.
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