Varying retrieval categoricity using hyperbolic geometry
The paper proposes a Vector Space Model over the Cayley-Klein Hyperbolic Geometry (referred to as Hyperbolic Information Retrieval = HIR) using a similarity measure derived from the hyperbolic distance. It is shown that the proposed model is equivalent with the classical Vector Space Model using Cosine measure with normalized weighting scheme. It is also shown that the categoricity of the new retrieval system can be varied by only modifying the radius of the hyperbolic space and without using a different weighting scheme and similarity measure, which is not the case in the VSM, where the same effect can only be obtained by both changing the weighting scheme and similarity measure at the expense of a more costly computation. Experiments are also reported to demonstrate and support the ideas, and they show that categoricity in HIR can be varied more than O(n) faster, where n is the number of index terms, than in the VSM.
hyperbolic geometry similarity measures information search and retrieval euclidean geometry cayley-klein model ranking order preservation