Evolving Systems

, Volume 8, Issue 3, pp 167–177 | Cite as

A new type of distance metric and its use for clustering

  • Xiaowei Gu
  • Plamen P. Angelov
  • Dmitry Kangin
  • Jose C. Principe
Original Paper


In order to address high dimensional problems, a new ‘direction-aware’ metric is introduced in this paper. This new distance is a combination of two components: (1) the traditional Euclidean distance and (2) an angular/directional divergence, derived from the cosine similarity. The newly introduced metric combines the advantages of the Euclidean metric and cosine similarity, and is defined over the Euclidean space domain. Thus, it is able to take the advantage from both spaces, while preserving the Euclidean space domain. The direction-aware distance has wide range of applicability and can be used as an alternative distance measure for various traditional clustering approaches to enhance their ability of handling high dimensional problems. A new evolving clustering algorithm using the proposed distance is also proposed in this paper. Numerical examples with benchmark datasets reveal that the direction-aware distance can effectively improve the clustering quality of the k-means algorithm for high dimensional problems and demonstrate the proposed evolving clustering algorithm to be an effective tool for high dimensional data streams processing.


Cosine similarity Distance metric Metric space Clustering High dimensional data streams processing 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Computing and CommunicationsLancaster University LancasterLancasterUK
  2. 2.Computational NeuroEngineering Laboratory, Department of Electrical and Computer EngineeringUniversity of FloridaGainesvilleUSA

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