Text categorization and semantic browsing with self-organizing maps on non-euclidean spaces

Abstract

This paper introduces a new type of Self-Organizing Map (SOM) for Text Categorization and Semantic Browsing. We propose a “hyperbolic SOM” (HSOM) based on a regular tesselation of the hy-perbolic plane, which is a non-euclidean space characterized by constant negative gaussian curvature. This approach is motivated by the observa-tion that hyperbolic spaces possess a geometry where the size of a neigh-borhood around a point increases exponentially and therefore provides more freedom to map a complex information space such as language into spatial relations. These theoretical findings are supported by our experi-ments, which show that hyperbolic SOMs can successfully be applied to text categorization and yield results comparable to other state-of-the-art methods. Furthermore we demonstrate that the HSOM is able to map large text collections in a semantically meaningful way and therefore allows a “semantic browsing” of text databases.