Representation and distance measure

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·  Continuous inputs

For a continuous input, the cuboid component is described by its lower left and its upper right bound l respectively r.


·  Nominal inputs

For a nominal input, the cuboid component is defined by a so called bit string b, that encodes, which symbols are covered by the cuboid component. The bit string has as many elements as the nominal input can take on different symbols. Each element corresponds to one of the possible symbols and can either have the value 0 or the value 1, whereas the latter means, that the symbol is covered by the bit string.


Figure: Cuboid representation and component wise distances in the case of two continuous inputs.

·  Continuous inputs

Take the minimum of the two lower left bounds of the two cuboid components that are generalized as the new lower left bound. Proceed the same way with the upper right bound, but use the maximum now. This is the most specific generalization with respect to the representation used.


·  Nominal inputs

When generalizing two cuboids, the bit string for a symbolic input is build by an OROperation, such that a symbol is covered by the generalized bit string, if it is covered by any of the two bit strings which are generalized.


Figure: Two examples to illustrate representation and generalization. The first three inputs are nominal and can take on the symbols a, b and c whereas the latter three inputs are continuous.
