The purpose of this chapter is to show how it is possible to efficiently extract the structure of a set of objects by use of the notion of proportional analogy.As a proportional analogy involves four objects, the very naïve approach to the problem, has basically a complexity of O(n4) for a given set of n objects. We show, under some conditions on proportional analogy, how to reduce this complexity to O(n2) by considering an equivalent problem, that of enumerating analogical clusters that are informative and not redundant. We further show how some improvements make the task tractable. We illustrate our technique with a task related with natural language processing, that of clustering Chinese characters. In this way, we re-discover the graphical structure of these characters.
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