Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data

Different aspects of the curse of dimensionality are known to present serious challenges to various machine-learning methods and tasks. This paper explores a new aspect of the dimensionality curse, referred to as hubness, that affects the distribution of k-occurrences: the number of times a point appears among the k nearest neighbors of other points in a data set. Through theoretical and empirical analysis involving synthetic and real data sets we show that under commonly used assumptions this distribution becomes considerably skewed as dimensionality increases, causing the emergence of hubs, that is, points with very high k-occurrences which effectively represent "popular" nearest neighbors. We examine the origins of this phenomenon, showing that it is an inherent property of data distributions in high-dimensional vector space, discuss its interaction with dimensionality reduction, and explore its influence on a wide range of machine-learning tasks directly or indirectly based on measuring distances, belonging to supervised, semi-supervised, and unsupervised learning families.