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Parallel Set charts are similar to Sankey Diagrams in the way they show flow and proportions, however Parallel Sets don't use arrows and they divide the flow-path at each displayed line-set.
Each line-set corresponds to a dimension/dataset, which its values/categories are represented in each line divide in that line-set. The width of each line and the flow-path that stems from it, is determined by the proportional fraction of the category total. Each flow-path can be coloured to show and compare the distribution between different categories.
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The development process of Parallel Sets can be found in Robert Kosara's papers:
Tools to Generate Visualisation