Identifying Clusters from Positive Data

The present work studies clustering from an abstract point of view and investigates its properties in the framework of inductive inference. Any class S considered is given by a hypothesis space, i.e., numbering, A0, A1, . . . of nonempty recursively enumerable (r.e.) subsets of N or Qk. A clustering task is a finite and nonempty set of r.e. indices of pairwise disjoint such sets. The class S is said to be clusterable if there is an algorithm which, for every clustering task I, converges in the limit on any text for i∈I Ai to a finite set J of indices of pairwise disjoint clusters such that j∈J Aj = i∈I Ai. A class is called semiclusterable if there is such an algorithm which finds a J with the last condition relaxed to j∈J Aj ⊇ i∈I Ai. The relationship between natural topological properties and clusterability is investigated. Topological properties can provide sufficient or necessary conditions for clusterability, but they cannot characterize it. On the one hand, many in...

• Type: Conference
• Year: 2004
• Where: ICGI
• Authors: John Case, Sanjay Jain, Eric Martin, Arun Sharma, Frank Stephan
• Keywords: Clustering Task, ICGI 2004, I∈i Ai, Natural Language Processing, Pairwise Disjoint