The Triangle Inequality versus Projection onto a Dimension in Determining Cosine Similarity Neighborhoods of Non-negative Vectors

  • Marzena Kryszkiewicz
Conference paper

DOI: 10.1007/978-3-642-32115-3_27

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7413)
Cite this paper as:
Kryszkiewicz M. (2012) The Triangle Inequality versus Projection onto a Dimension in Determining Cosine Similarity Neighborhoods of Non-negative Vectors. In: Yao J. et al. (eds) Rough Sets and Current Trends in Computing. RSCTC 2012. Lecture Notes in Computer Science, vol 7413. Springer, Berlin, Heidelberg

Abstract

In many applications, objects are represented by non-negative vectors and cosine similarity is used to measure their similarity. It was shown recently that the determination of the cosine similarity of two vectors can be transformed to the problem of determining the Euclidean distance of normalized forms of these vectors. This equivalence allows applying the triangle inequality to determine cosine similarity neighborhoods efficiently. Alternatively, one may apply the projection onto a dimension to this end. In this paper, we prove that the triangle inequality is guaranteed to be a pruning tool, which is not less efficient than the projection in determining neighborhoods of non-negative vectors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marzena Kryszkiewicz
    • 1
  1. 1.Institute of Computer ScienceWarsaw University of TechnologyWarsawPoland

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