Vector-Distance and Neighborhood Development for High Dimensional Data

This paper presents a novel distance concept, Vector-Distance (VD) for high dimensional data. VD extends traditional scalar-distance to a vector-like fashion by collecting multi partial distances from diverse angles. These partial distances are derived from random projections, and they preserve individual features of dimensions as much as possible. Based on VD definition, a method family for neighborhood development is proposed, where methods consist of some norm definitions and certain constrains specified for various purposes. Experiments on real datasets verify the quality of neighborhoods produced by the proposed method family better or competitive with the neighborhood produced by the state of the art.