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OFAI-TR-2014-03 ( 120kB PDF file)

Choosing the Metric in High-Dimensional Spaces Based on Hub Analysis

Dominik Schnitzer, Arthur Flexer

To avoid the undesired effects of distance concentration in high-dimensional spaces, previous work has already advocated the use of fractional ℓp norms instead of the ubiquitous Euclidean norm. Closely related to concentration is the emergence of hub and anti-hub objects. Hub objects have a small distance to an exceptionally large number of data points while anti-hubs lie far from all other data points. The contribution of this work is an empirical examination of concentration and hubness, resulting in an unsupervised approach for choosing an ℓp norm by minimizing hubs while simultaneously maximizing nearest neighbor classification.

Keywords: Hubness, Concentration of distances, High-dimensional data analysis

Citation: Schnitzer D., Flexer A.: Choosing the Metric in High-Dimensional Spaces Based on Hub Analysis, in Proceedings of the 22nd European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium, 2014.