A Novel Distance Definition Based on Multi Partial Distance Information

Abstract

This paper presents a novel distance concept, Vectored-Distance (VD) for high dimensional data. VD extends traditional scalar distance definition to a vector-styled fashion by extracting multi local distance information from diverse angles. These partial distances act as entries of VD, and they preserve individual features of involved dimensions as much as possible. That addresses the drawback of scalar distance that only reveals the difference among data in a single manner. Then an algorithm of neighborhood formulation for high dimensional data is proposed by combining the VD and the Locality-Sensitive Hashing idea, named as VDLSH. Experiments on real datasets verify the performance of VD and VDLSH through checking the quality of the neighborhoods produced by VDLSH.