On the Vulnerability of Retrieval in High Intrinsic Dimensionality Neighborhood

Abstract

This article investigates the vulnerability of the nearest neighbors search, which is a pivotal tool in pattern analysis and data science. The vulnerability is gauged as the relative amount of perturbation that an attacker needs to add to a dataset point in order to modify its proximity to a given query. The statistical distribution of the relative amount of perturbation is derived from simple assumptions, outlining the key factor that drives its typical values: The higher the intrinsic dimensionality, the more vulnerable is the nearest neighbors search. Experiments on six large-scale datasets validate this model up to some outliers, which are explained as violations of the assumptions.