Random Manhattan Integer Indexing: Incremental L1 Normed Vector Space Construction

Behrang Q. Zadeh, Siegfried Handschuh

Abstract: Vector space models (VSMs) are mathematically well-defined frameworks that have been widely used in the distributional approaches to semantics. In VSMs, highdimensional vectors represent linguistic entities. In an application, the similarity of vectors—and thus the entities that they represent—is computed by a distance formula. The high dimensionality of vectors, however, is a barrier to the performance of methods that employ VSMs. Consequently, a dimensionality reduction technique is employed to alleviate this problem. This paper introduces a novel technique called Random Manhattan Indexing (RMI) for the construction of ‘1 normed VSMs at reduced dimensionality. RMI combines the construction of a VSM and dimension reduction into an incremental and thus scalable two-step procedure. In order to attain its goal, RMI employs the sparse Cauchy random projections. We further introduce Random Manhattan Integer Indexing (RMII): a computationally enhanced version of RMI. As shown in the reported experiments, RMI and RMII can be used reliably to estimate the ‘1 distances between vectors in a vector space of low dimensionality.