A Simplicial Complex, a Hypergraph, Structure in the latent Semantic Space of Document Clustering

This paper presents a novel approach to document clustering based on some geometric structure in Combinatorial Topology. Given a set of documents, the set of associations among frequently co-occurring terms in documents forms naturally a simplicial complex. Our general thesis is each connected component of this simplicial complex represents a concept in the collection. Based on these concepts, documents can be clustered into meaningful classes. However, in this paper, we attack a softer notion, instead of connected components, we use maximal simplexes of highest dimension as representative of connected components, the concept so defined is called maximal primitive concepts.

Experiments with three different data sets from Web pages and medical literature have shown that the proposed unsupervised clustering approach performs significantly better than traditional clustering algorithms, such as k-means, AutoClass and Hierarchical Clustering (HAG). This abstract geometric model seems have captured the latent semantic structure of documents.

Keywords: Document clustering; Association rules; Topology; Hierarchical clustering; Simplicial complex