Granulate and Conquer : Clustering Web Pages Semantically using Combinatorial Topology

Granulation is a natural problem-solving methodology deeply rooted in human thinking; Human body is granulated into head, neck, and etc. The notion is intrinsically fuzzy, vague and imprecise. Previously, we have proposed mathematical models and illustrate the idea in college calculus, fuzzy set theory, and web intelligence. In this paper, we will focus on how to use the notion to cluster web pages. A set of documents is a knowledge representation some human thoughts; The thoughts will be called the Latent Semantic Space. In this paper, we will granulate the Latent Semantic Space into a polyhedron. As it is a geometric, hence, a language independent, representation. S one can identify the semantic equivalency between a set of English documents and, say, its Chinese version without direct translation. A polyhedron is a closed and bounded subset of an Euclidean space that has a combinatorial structure, called a simplicial complex. In this representation the structure of concepts can be captured by this geometry: Primitive concepts, concepts, and the idea are represented by sub-polyhedra of simplexes, connected components, and the simplicial complex respectively. Based on these structures, documents can be clustered into meaningful classes. By applying this method to a return of some current search engine, one may provide users a more semantically oriented search results.

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