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What are Generalizing Exemplars?
Generalized exemplars are the rectangular scope of instance area, known as hyperrectangles because they are high-dimensional. When defining new instances it is essential to convert the distance function to enable the distance to a hyperrectangle to be computed.
When a new exemplar is defined correctly, it is generalized by directly merging it with the nearest exemplar of a similar class. The nearest exemplar can be an individual instance or a hyperrectangle.
In this method, a new hyperrectangle is generated that covers the previous and the new instance. The hyperrectangle is expanded to surround the new instance. Lastly, if the prediction is false and it was a hyperrectangle that was answerable for the incorrect prediction, the hyperrectangle’s borders are modified so that it decreases away from the fresh instance.
It is essential to determine at the outset whether overgeneralization caused by occupying or overlapping hyperrectangles is to be allowed or not. If it is to be prevented, a check is created before generalizing a new instance to view whether some regions of the feature area conflict with the suggested new hyperrectangle. If the generalization is nullified and the example is saved verbatim. Overlapping hyperrectangles are precisely related to positions in which the same instance is protected by multiple rules in a ruleset.
In some schemes, generalized exemplars can be fixed in that they can be completely included within one another likewise that in some descriptions rules can have exceptions.
This second-chance structure boost nesting of hyperrectangles. If an instance falls within a rectangle of the wrong class that includes an exemplar of a similar class, the two are generalized into a new “exception” hyperrectangle nested inside the initial one. For fixed generalized exemplars, the learning procedure generally starts with a few seed instances to avoid some instances of the same class from being generalized into an individual rectangle that covers a few problem areas.
With generalized exemplars, it is essential to generalize the distance function to calculate the distance from an instance to a generalized exemplar and another instance. The distance from an instance to a hyperrectangle is described to be zero if the point lies inside the hyperrectangle.
The simplest way to generalize the distance function to calculate the distance from an exterior point to a hyperrectangle is to select the nearest instance within it and to compute the distance to that. However, this decreases the advantage of generalization because it reintroduces dependence on a specific single example.
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