A comprehensive empirical comparison of hubness reduction in high-dimensional spaces

Hubness is an aspect of the curse of dimensionality related to the distance concentration effect. Hubs occur in high-dimensional data spaces as objects that are particularly often among the nearest neighbors of other objects. Conversely, other data objects become antihubs, which are rarely or never nearest neighbors to other objects. Many machine learning algorithms rely on nearest neighbor search and some form of measuring distances, which are both impaired by high hubness. Degraded performance due to hubness has been reported for various tasks such as classification, clustering, regression, visualization, recommendation, retrieval and outlier detection. Several hubness reduction methods based on different paradigms have previously been developed. Local and global scaling as well as shared neighbors approaches aim at repairing asymmetric neighborhood relations. Global and localized centering try to eliminate spatial centrality, while the related global and local dissimilarity measures are based on density gradient flattening. Additional methods and alternative dissimilarity measures that were argued to mitigate detrimental effects of distance concentration also influence the related hubness phenomenon. In this paper, we present a large-scale empirical evaluation of all available unsupervised hubness reduction methods and dissimilarity measures. We investigate several aspects of hubness reduction as well as its influence on data semantics which we measure via nearest neighbor classification. Scaling and density gradient flattening methods improve evaluation measures such as hubness and classification accuracy consistently for data sets from a wide range of domains, while centering approaches achieve the same only under specific settings.