Granular Computing and Web Processing: Representing Documents in Polyhedron

Summary form only given. Granular computing (GrC) is a pragmatic approach to data and knowledge engineering. Roughly, it is a methodology that involves elements (data) and subsets (knowledge). We will illustrate the idea via a web application. In traditional web processing, we often represent a document by a set of keywords. In GrC, let us call it granular representation, we include the knowledge. More precisely, a document is not only represented by its keywords, but also by its granules. Here by a granule we mean a keyword association, which is a set of frequent co-occurring near by keywords. For a trivial example, the association, "Wall street," as a financial concept, is in the granular representation. The granular representation has an interesting geometric interpretation. We can regard the set of keywords as a set of vertices, and the set of keyword associations as a set of simplexes. Interestingly in such a translation, the a priori principle is converted into the closed condition of simplical complexes. In other words, the collection of keywords and keyword associations is an abstract simplicial complex in algebraic topology.