Distinguishing and Classifying from n-ary Properties

We present a hierarchical classification based on n-ary relations of the entities. Starting from the finest partition that can be obtained from the attributes, we distinguish between entities having the same attributes by using relations between entities. The classification that we get is thus a refinement of this finest partition. It can be computed in O(n + m <Superscript>2</Superscript>) space and O(n · p · m <Superscript>5/2</Superscript>) time, where n is the number of entities, p the number of classes of the resulting hierarchy (p is the size of the output; p > 2n) and m the maximum number of relations an entity can have (usually, m ≪ n). So we can treat sets with millions of entities. Copyright Classification Society of North America 2014